When typing into the search field, the cursor is moved around the editor, displaying the results of an incremental search.
When completely emptying the "search"-field, the cursor should be reset to what it was before entering the find/field.

Here is a video showcasing my frustration with this behavior:

By "accidentally" pressing "0" while inside of the search field, I am suddenly on the complete other end of the file.

VSCode handles this case exactly like the current Overlay does. I could not find a plausible reason why, I believe that this is a genuine pain point where as you want to be able return to the position where you started searching before typing anything into the search bar.