how to display search term in the template full site editor

I don’t think there’s a core way to do that in WordPress 5.9 ..

So for now, you can use a custom shortcode which returns the inner HTML/content for the heading (e.g. Search Results for <search query> with translation/gettext applied), and then use <h1>[your-shortcode]</h1> in your template.

Here’s a sample shortcode function that you can try:

add_shortcode( 'your-shortcode', function () {
    /* translators: %s: Search query/keyword. */
    return sprintf(
        __( 'Search Results for "%s"', 'text-domain' ),
        esc_attr( get_search_query() )
    );
} );

You can also create another shortcode which returns just the search query, if you want to, but remember that you should use get_search_query() and not the_search_query() which echo the output, hence the former should be used in shortcode function which generally should not echo anything.