This includes:
* Removing the deprecated `screen_icon()` function call.
* Replacing the deprecated `get_current_theme()` function call with `get_option( 'current_theme' )`.
* Using `wp_get_theme()->display( 'Name' )` explicitly instead of relying on `WP_Theme`'s `__toString()` method, for clarity.
Follow-up to [6334], [20039], [20040], [20042], [20508], [26537], [41274].
Props Presskopp, cu121, viralsampat, costdev, tomjdv, sabernhardt, SergeyBiryukov.
Fixes#54833.
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