Plex doesn’t read all embedded tags, just a subset that it generally needs to identify an album. There seems to be an addiction to marketing hype that prevents them from being completely open about this up-front. There are a couple of feature requests to expand this.
Tag support for ROBUST music library organization
By Composer
I believe the list below is complete, or nearly so, as to which tags Plex actually reads:
Album Title
Track Title
Artist (artist of each individual track) see below
Album Artist see below
Track Number
Disc Number
Recording/Release date or Year
Album sort order
Album Artist sort order
Genre
embedded album cover
“Composer” is definitely the most conspicuous absence from that list. Plex doesn’t do classical music very well because of it.
Moods definitely come from online sources (I thought it was Last.FM, but it may be AllMusic).
Just this morning I reported that Plex is not respecting the “Genres: Embedded Tags” setting. I think that’s a recent bug. I’ve seen it work correctly in the past.