Go to Tools > Rip CD
In the resulting Rip CD popup window, enter appropriate data into the Album artist, Artist, Composer etc. fields
Click on Start Rip
Data in the Publisher field is not saved to the resulting media files. The other fields are saved.
This happens consistently across a range of CDs.
Under Preferences > CD Ripping:
Encode as: FLAC
Profile: Maximum compression
Encoding parameters: -s -5 -o [outputfile] -
MusicBee version used: 3.5.8402
Many thanks Steven. I really appreciate MusicBee.