I use MusicBrainz Picard to tag my media for plex. When I started using plex with my music media I initially had trouble with the sorting tags and found it best to ensure tags “albumartistsort” and “artistsort” match the sorting I wanted from my artists.
I ended up scripting this in MusicBrainz setting the albumartistsort and artistsort tags to be the same value as albumartist. This works for me but can you use any value you want yourself.
$set(artistsort,%albumartist%)
$set(albumartistsort,%albumartist%)
Here are the tags from one of my albums.

BTW… otto makes a great point regarding “Sort Artist tag is only read if an album by that artist is being added for the first time”. For this reason I would recommend a full plex dance of the entire artist and all its albums when changing artist level tags, like sort. That way you can be sure plex will pick them up correctly.