Olá,
Se entendi corretamente, você gostaria de adicionar o ícone de busca aqui na página de busca 
Acho que, para isso, você precisará sobrescrever o template do Discourse.
Veja como fazer: Sobrescrevendo templates do Discourse, mas sugiro ler toda a documentação.
Neste caso, ficaria mais ou menos assim. Primeiro, você precisa encontrar o template da página de busca. Aqui estão os templates: https://github.com/discourse/discourse/tree/main/app/assets/javascripts/discourse/app/templates
O template que estamos procurando é o full-page-search.hbs, e podemos ver claramente qual parte devemos editar para fazer essa alteração.
Esta é a parte do cabeçalho do template que vamos editar… mas isso vem um pouco mais tarde…
<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>
Agora que sabemos, pela documentação acima, devemos começar assim:
O template vai para a seção header.
<script type="text/x-handlebars" data-template-name="full-page-search">
</script>
Depois, temos que copiar todo o template para dentro:
Fica assim
<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>
Agora podemos editar a parte do cabeçalho que mencionei antes. Neste caso, é uma alteração bem simples, mas você pode fazer alterações mais complexas. Certifique-se de que seu template personalizado esteja sempre atualizado. Se houver alguma alteração no template principal, você também deve atualizar seu template personalizado para que tudo funcione corretamente. 
Neste caso, basta adicionar um ícone {{d-icon "search"}} antes do título da página completa e antes da contagem de resultados.
O template completo fica assim
<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 isso ajude
