I have had similar issues and found a workaround for fixing it and the fix sticking in my server. I have a number of artists and albums where the tags are butchered to death, way to lazy to go through the entire collection to specifically diagnose each one, so let plex do the lifting, I know my artist as that’s easily attainable from my media library folders (I do keep everything stored in the proper locations, tags are just a pain).
For example, You have a an artist not matching and when trying to use the last FM client it returns no results (sometimes it does, however its become so unreliable i just use this method every time). Edit the artist in plex by clicking pencil, edit the artist name and sort name to match the artist, save(Make sure the lock icon over the name is now orange, this will prevent plex from auto updating that info), now match with last.fm, magically last fm returns the results that it was not before.
Seeing this behavior and how the box auto fills when trying to search I think the problem lies in plex, It is taking the artist info only from what it is labeled as, and when typing in a search it does not respect it. I have nothing to back that other then my experience, but hopefully might give one of the plex team members a trail to start on.