Hi,
I always mess with search for music: looking for an artist in album section for example.
I could be nice to keep the search words while switching category 
Best^^
Paul
Sorry but not really possible. When you click on an artist you get the album list the search should be kept at that deeper level.
Same for the search used as filter they are kept per screen but restored. If using the same for all It start to became a big mess to handle.
If you always mix, just always use the global search in left menu so you have both.