I meant playlist, sorry.
When changing between playlists (and other node types), MusicBee keeps the previous search term that was applied to filter the selected playlist.
I'm not aware of this behaviour having changed recently and can't see anything in the release notes.
I'm also sure there's no setting that controls it. The only settings related to the Search field are those in the little magnifying glass menu.
So the suggestion remains the same. I can see how it would be handy to search for a given track across all playlists.
Bee excellent to each other...