Hola,
Si he entendido correctamente, te gustaría añadir un icono de búsqueda aquí en la página de búsqueda 
Creo que para esto necesitas sobrescribir la plantilla de Discourse.
Así es como se hace: Sobrescribir plantillas de Discourse, pero te sugiero que leas toda la documentación.
En este caso, se vería algo así. Primero debes encontrar la plantilla de la página de búsqueda. Aquí están las plantillas: https://github.com/discourse/discourse/tree/main/app/assets/javascripts/discourse/app/templates
La plantilla que buscamos es full-page-search.hbs y podemos ver claramente qué parte debemos editar para realizar este cambio.
Esta es la parte del encabezado de la plantilla que editaremos… pero eso será un poco más adelante…
<h1 class="search-page-heading">
{{#if this.hasResults}}
<div class="result-count" id="search-result-count" aria-live="polite">
{{html-safe this.resultCountLabel}}
</div>
{{else}}
{{i18n "search.full_page_title"}}
{{/if}}
</h1>
Ahora, según la documentación anterior, debemos comenzar así:
La plantilla va a la sección header.
<script type="text/x-handlebars" data-template-name="full-page-search">
</script>
Luego, debemos copiar la plantilla completa dentro:
Se ve así
<script type="text/x-handlebars" data-template-name="full-page-search">
<DSection @pageClass="search" @class="search-container">
<ScrollTracker @name="full-page-search" @tag={{this.searchTerm}} @class="hidden" />
<div class="search-header" role="search">
<h1 class="search-page-heading">
{{#if this.hasResults}}
<div class="result-count" id="search-result-count" aria-live="polite">
{{html-safe this.resultCountLabel}}
</div>
{{else}}
{{i18n "search.full_page_title"}}
{{/if}}
</h1>
<div class="search-bar">
<SearchTextField @value={{this.searchTerm}} @class="full-page-search search no-blur search-query" @aria-label={{i18n "search.search_term_label"}} @enter={{action "search" (hash collapseFilters=true)}} @hasAutofocus={{this.hasAutofocus}} @aria-controls="search-result-count" />
<ComboBox @id="search-type" @value={{this.search_type}} @content={{this.searchTypes}} @onChange={{action (mut this.search_type)}} @options={{hash
castInteger=true
}} />
<DButton @action={{action "search" (hash collapseFilters=true)}} @icon="search" @label="search.search_button" @class="btn-primary search-cta" @ariaLabel="search.search_button" @disabled={{this.searchButtonDisabled}} />
</div>
{{#if this.usingDefaultSearchType}}
{{!-- context is only provided when searching from mobile view --}}
{{#if this.context}}
<div class="search-context">
<label>
<Input @type="checkbox" name="searchContext" @checked={{this.searchContextEnabled}} /> {{this.searchContextDescription}}
</label>
</div>
{{/if}}
<div class="search-filters">
<SearchAdvancedOptions @searchTerm={{readonly this.searchTerm}} @onChangeSearchTerm={{action (mut this.searchTerm)}} @search={{action "search" (hash collapseFilters=true)}} @searchButtonDisabled={{this.searchButtonDisabled}} @expandFilters={{this.expandFilters}} />
</div>
{{/if}}
<div class="search-notice">
{{#if this.invalidSearch}}
<div class="fps-invalid">
{{i18n "search.too_short"}}
</div>
{{/if}}
</div>
</div>
<div class="search-advanced">
{{#if this.hasResults}}
{{#if this.usingDefaultSearchType}}
<div class={{this.searchInfoClassNames}} role="region" ariaLabel={{i18n "search.sort_or_bulk_actions"}}>
{{#if this.canBulkSelect}}
<DButton @icon="list" @class="btn-default bulk-select" @title="topics.bulk.toggle" @action={{action "toggleBulkSelect"}} />
{{#if this.selected}}
<DButton @class="btn-default bulk-select-btn" @selected={{this.selected}} @action={{action "showBulkActions"}} @icon="wrench" />
{{/if}}
{{/if}}
{{#if this.bulkSelectEnabled}}
{{#if this.hasUnselectedResults}}
<DButton @icon="check-square" @class="btn-default" @action={{action "selectAll"}} @label="search.select_all" />
{{/if}}
{{#if this.hasSelection}}
<DButton @icon="far-square" @class="btn-default" @action={{action "clearAll"}} @label="search.clear_all" />
{{/if}}
{{/if}}
<div class="sort-by inline-form">
<label>
{{i18n "search.sort_by"}}
</label>
<ComboBox @value={{this.sortOrder}} @content={{this.sortOrders}} @onChange={{action (mut this.sortOrder)}} @id="search-sort-by" @options={{hash
castInteger=true
}} />
</div>
</div>
{{/if}}
{{/if}}
<PluginOutlet @name="full-page-search-below-search-info" @tagName="span" @connectorTagName="div" @args={{hash search=this.searchTerm}} />
{{#if this.searching}}
{{loading-spinner size="medium"}}
{{else}}
<div class="search-results" role="region">
<LoadMore @selector=".fps-result" @action={{action "loadMore"}}>
{{#if this.usingDefaultSearchType}}
<SearchResultEntries @posts={{this.model.posts}} @bulkSelectEnabled={{this.bulkSelectEnabled}} @selected={{this.selected}} @highlightQuery={{this.highlightQuery}} @searchLogId={{this.model.grouped_search_result.search_log_id}} />
<ConditionalLoadingSpinner @condition={{this.loading}}>
{{#unless this.hasResults}}
{{#if this.searchActive}}
<h3>{{i18n "search.no_results"}}</h3>
{{#if this.model.grouped_search_result.error}}
<div class="warning">
{{this.model.grouped_search_result.error}}
</div>
{{/if}}
{{#if this.showSuggestion}}
<div class="no-results-suggestion">
{{i18n "search.cant_find"}}
{{#if this.canCreateTopic}}
<a href {{action "createTopic" this.searchTerm}}>{{i18n "search.start_new_topic"}}</a>
{{#unless this.siteSettings.login_required}}
{{i18n "search.or_search_google"}}
{{/unless}}
{{else}}
{{i18n "search.search_google"}}
{{/if}}
</div>
<GoogleSearch @searchTerm={{this.searchTerm}} />
{{/if}}
{{/if}}
{{/unless}}
{{#if this.hasResults}}
<h3 class="search-footer">
{{#if this.model.grouped_search_result.more_full_page_results}}
{{#if this.isLastPage}}
{{i18n "search.more_results"}}
{{/if}}
{{else}}
{{i18n "search.no_more_results"}}
{{/if}}
</h3>
{{/if}}
</ConditionalLoadingSpinner>
{{else}}
<ConditionalLoadingSpinner @condition={{this.loading}}>
{{#if this.hasResults}}
{{#if this.model.categories.length}}
<h4 class="category-heading">
{{i18n "search.categories"}}
</h4>
<div class="category-items">
{{#each this.model.categories as |category|}}
{{category-link category extraClasses="fps-category-item"}}
{{/each}}
</div>
{{/if}}
{{#if this.model.tags.length}}
<h4 class="tag-heading">
{{i18n "search.tags"}}
</h4>
<div class="tag-items">
{{#each this.model.tags as |tag|}}
<div class="fps-tag-item">
<a href={{tag.url}}>
{{tag.id}}
</a>
</div>
{{/each}}
</div>
{{/if}}
{{#if this.model.users}}
<div class="user-items">
{{#each this.model.users as |user|}}
<UserLink @user={{user}} @class="fps-user-item">
{{avatar user imageSize="large"}}
<div class="user-titles">
{{#if user.name}}
<span class="name">
{{user.name}}
</span>
{{/if}}
<span class="username">
{{user.username}}
</span>
</div>
</UserLink>
{{/each}}
</div>
{{/if}}
{{else}}
{{#if this.searchActive}}
<h3>{{i18n "search.no_results"}}</h3>
{{/if}}
{{/if}}
</ConditionalLoadingSpinner>
{{/if}}
</LoadMore>
</div>
{{/if}}
</div>
</DSection>
</script>
Ahora podemos editar la parte del encabezado que mencioné antes. En este caso, es un cambio muy sencillo, pero puedes realizar cambios más complejos. Asegúrate de que tu plantilla personalizada siempre esté actualizada. Si hay algún cambio en la plantilla principal, también debes actualizar tu plantilla personalizada para que todo funcione correctamente. 
En este caso, simplemente añadimos un icono {{d-icon "search"}} antes del título de la página completa y antes del recuento de resultados.
La plantilla completa se ve así
<script type="text/x-handlebars" data-template-name="full-page-search">
<DSection @pageClass="search" @class="search-container">
<ScrollTracker @name="full-page-search" @tag={{this.searchTerm}} @class="hidden" />
<div class="search-header" role="search">
<h1 class="search-page-heading">
{{#if this.hasResults}}
<div class="result-count" id="search-result-count" aria-live="polite">
{{d-icon "search"}}
{{html-safe this.resultCountLabel}}
</div>
{{else}}
{{d-icon "search"}}
{{i18n "search.full_page_title"}}
{{/if}}
</h1>
<div class="search-bar">
<SearchTextField @value={{this.searchTerm}} @class="full-page-search search no-blur search-query" @aria-label={{i18n "search.search_term_label"}} @enter={{action "search" (hash collapseFilters=true)}} @hasAutofocus={{this.hasAutofocus}} @aria-controls="search-result-count" />
<ComboBox @id="search-type" @value={{this.search_type}} @content={{this.searchTypes}} @onChange={{action (mut this.search_type)}} @options={{hash
castInteger=true
}} />
<DButton @action={{action "search" (hash collapseFilters=true)}} @icon="search" @label="search.search_button" @class="btn-primary search-cta" @ariaLabel="search.search_button" @disabled={{this.searchButtonDisabled}} />
</div>
{{#if this.usingDefaultSearchType}}
{{!-- context is only provided when searching from mobile view --}}
{{#if this.context}}
<div class="search-context">
<label>
<Input @type="checkbox" name="searchContext" @checked={{this.searchContextEnabled}} /> {{this.searchContextDescription}}
</label>
</div>
{{/if}}
<div class="search-filters">
<SearchAdvancedOptions @searchTerm={{readonly this.searchTerm}} @onChangeSearchTerm={{action (mut this.searchTerm)}} @search={{action "search" (hash collapseFilters=true)}} @searchButtonDisabled={{this.searchButtonDisabled}} @expandFilters={{this.expandFilters}} />
</div>
{{/if}}
<div class="search-notice">
{{#if this.invalidSearch}}
<div class="fps-invalid">
{{i18n "search.too_short"}}
</div>
{{/if}}
</div>
</div>
<div class="search-advanced">
{{#if this.hasResults}}
{{#if this.usingDefaultSearchType}}
<div class={{this.searchInfoClassNames}} role="region" ariaLabel={{i18n "search.sort_or_bulk_actions"}}>
{{#if this.canBulkSelect}}
<DButton @icon="list" @class="btn-default bulk-select" @title="topics.bulk.toggle" @action={{action "toggleBulkSelect"}} />
{{#if this.selected}}
<DButton @class="btn-default bulk-select-btn" @selected={{this.selected}} @action={{action "showBulkActions"}} @icon="wrench" />
{{/if}}
{{/if}}
{{#if this.bulkSelectEnabled}}
{{#if this.hasUnselectedResults}}
<DButton @icon="check-square" @class="btn-default" @action={{action "selectAll"}} @label="search.select_all" />
{{/if}}
{{#if this.hasSelection}}
<DButton @icon="far-square" @class="btn-default" @action={{action "clearAll"}} @label="search.clear_all" />
{{/if}}
{{/if}}
<div class="sort-by inline-form">
<label>
{{i18n "search.sort_by"}}
</label>
<ComboBox @value={{this.sortOrder}} @content={{this.sortOrders}} @onChange={{action (mut this.sortOrder)}} @id="search-sort-by" @options={{hash
castInteger=true
}} />
</div>
</div>
{{/if}}
{{/if}}
<PluginOutlet @name="full-page-search-below-search-info" @tagName="span" @connectorTagName="div" @args={{hash search=this.searchTerm}} />
{{#if this.searching}}
{{loading-spinner size="medium"}}
{{else}}
<div class="search-results" role="region">
<LoadMore @selector=".fps-result" @action={{action "loadMore"}}>
{{#if this.usingDefaultSearchType}}
<SearchResultEntries @posts={{this.model.posts}} @bulkSelectEnabled={{this.bulkSelectEnabled}} @selected={{this.selected}} @highlightQuery={{this.highlightQuery}} @searchLogId={{this.model.grouped_search_result.search_log_id}} />
<ConditionalLoadingSpinner @condition={{this.loading}}>
{{#unless this.hasResults}}
{{#if this.searchActive}}
<h3>{{i18n "search.no_results"}}</h3>
{{#if this.model.grouped_search_result.error}}
<div class="warning">
{{this.model.grouped_search_result.error}}
</div>
{{/if}}
{{#if this.showSuggestion}}
<div class="no-results-suggestion">
{{i18n "search.cant_find"}}
{{#if this.canCreateTopic}}
<a href {{action "createTopic" this.searchTerm}}>{{i18n "search.start_new_topic"}}</a>
{{#unless this.siteSettings.login_required}}
{{i18n "search.or_search_google"}}
{{/unless}}
{{else}}
{{i18n "search.search_google"}}
{{/if}}
</div>
<GoogleSearch @searchTerm={{this.searchTerm}} />
{{/if}}
{{/if}}
{{/unless}}
{{#if this.hasResults}}
<h3 class="search-footer">
{{#if this.model.grouped_search_result.more_full_page_results}}
{{#if this.isLastPage}}
{{i18n "search.more_results"}}
{{/if}}
{{else}}
{{i18n "search.no_more_results"}}
{{/if}}
</h3>
{{/if}}
</ConditionalLoadingSpinner>
{{else}}
<ConditionalLoadingSpinner @condition={{this.loading}}>
{{#if this.hasResults}}
{{#if this.model.categories.length}}
<h4 class="category-heading">
{{i18n "search.categories"}}
</h4>
<div class="category-items">
{{#each this.model.categories as |category|}}
{{category-link category extraClasses="fps-category-item"}}
{{/each}}
</div>
{{/if}}
{{#if this.model.tags.length}}
<h4 class="tag-heading">
{{i18n "search.tags"}}
</h4>
<div class="tag-items">
{{#each this.model.tags as |tag|}}
<div class="fps-tag-item">
<a href={{tag.url}}>
{{tag.id}}
</a>
</div>
{{/each}}
</div>
{{/if}}
{{#if this.model.users}}
<div class="user-items">
{{#each this.model.users as |user|}}
<UserLink @user={{user}} @class="fps-user-item">
{{avatar user imageSize="large"}}
<div class="user-titles">
{{#if user.name}}
<span class="name">
{{user.name}}
</span>
{{/if}}
<span class="username">
{{user.username}}
</span>
</div>
</UserLink>
{{/each}}
</div>
{{/if}}
{{else}}
{{#if this.searchActive}}
<h3>{{i18n "search.no_results"}}</h3>
{{/if}}
{{/if}}
</ConditionalLoadingSpinner>
{{/if}}
</LoadMore>
</div>
{{/if}}
</div>
</DSection>
</script>
Espero que esto te ayude.
