So, I don't know if there's an option for this as I haven't found one yet.
Take it as a suggestion if it doesn't exist yet and an update to the FAQ if it does.
In Rekordbox, when I have something typed into the search bar and then switch to a different folder/playlist it clears the input of the search bar.
This seems like a protection maybe to avoid loading times or something...
HOWEVER, it does obstruct flexible/efficient searching.
Would be nice to have the option to keep the input in the search bar as you switch folders/playlists.
If there's a problem when switching folders (it taking a long time to load because it starts searching the whole folder for the search bar input that's still there), my next suggestion would be to keep the text in the search bar and then confirm the search by clicking the search icon or going into the search bar and pressing enter.
(currently if you click the search icon or the triangle next to it you get the settings for the searching:
search all categories, search by artist, by title, by album, etc.
I'd suggest turning the search icon settings click into a hover and clicking the icon to be a 'enter')
If the text isn't as clear I could provide a few sketches and screenshots of the rekordbox layout to give a more visual idea of what I mean.