Elusive track metadata for recording

Have a look at
“Use release relationships” and “Use track relationships” in Picard->Options->Options->Metadata.

Have you got these enabled/checked?

I’ll grab this opportunity to maybe slightly flatten the learning curve that Picard and Musicbrainz presents.
Maybe you won’t find Picard and Musicbrainz as difficult as I did.

An album or a single is called a Release.
A Release has Tracks. (A Release can have a Release Artist.)
Those tracks have a Recording on them. (A Recording can have a Recording Artist (aka “performer”.)
Other Releases can have the same Recording.
A Work is a musical piece that has been named and can be performed again. (A Work can have a composer/lyricist/writer etc.)

AIUI there is more detail around Works available through the
Classical Extras plug-in by MetaTunes but maybe you don’t need the extra level of detail.