Hello,
If I understand correctly you would like to add search icon here on search page 
I think for this you need to override the Discourse template.
Here is how to do it: Overriding Discourse templates but I suggest to read the all documentation.
In this case is looks something like this. First you have to find the search page template. Here are the templates: discourse/app/assets/javascripts/discourse/app/templates at main · discourse/discourse · GitHub
The template we looking for is the full-page-search.hbs and we can clearly see which part we should edit to make this change.
This is the heading part of the template which we will edit…but that is a little bit later…
<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>
Now we know from the doc above, we should start like this:
The template goes to the header section.
<script type="text/x-handlebars" data-template-name="full-page-search">
</script>
Than we have to copy the full template inside:
Looks like this
<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>
Now we can edit the heading part what I mentioned before. In this case this is a really simple change but you can make more complex changes. Be sure your custom template is always up to date. If there is any change in the core template you should update your custom template as well to works everything fine. 
In this case we just add an icon {{d-icon "search"}} before full page title and before results count.
The full template looks like this
<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>
Hope this helps
