EAC wasn’t able to find a commercial CD I have when it did its MusicBrainz lookup. Eventually I found it with Picard and the " Search by release" lookup on the website. I was able to get that information back into Picard. Now, how do I get all the information from Picard to EAC, so that when I use EAC to rip the CD to MP3 files, the tags will be there? Is there either some copy/paste feature or ID linking system that can do that?
Submit Disc ID in Picard (add a new MusicBrainz Release if the existing MusicBrainz Release is not the same as your copy), then re-lookup in EAC.
See also How to Add Disc IDs - MusicBrainz
and the Picard specific instructions Attaching a Disc ID to a Release — MusicBrainz Picard v2.7.3 documentation
If there are multiple release versions, make sure you pick the exact version you have (by matching barcode, cat. no., cover art etc.)