The Rosamund theme has a search drawer with a search form + a list of labels. You can click on the search icon in the top menu to expand it.
If you want to display specific labels in the "Browse by Category" section, go to Layout > scroll down to "Search Drawer" > open the "Browse by Category" widget > check "Selected Labels" > uncheck the labels you don't want to display in the widget.
Keep in mind that labels will only appear in the widget if they have been used in at least one published post.
The search form is already added, but here's the HTML if you need it:
<form action="/search" class="search-form" method="get">
<input class="search-input" name="q" placeholder="Search" type='text' value=""/>
<button class="search-submit" type="submit" value="Search"><i class="fas fa-search"></i></button>
</form>