I am not advocating piracy here. This is just a method to remove the purchased flag from Apple Music/iTunes downloaded files, and make them show up as normal AAC files if you have some reason to do so.
The shotgun approach is to just remove all the meta-data from the stream. This is simple enough with my favorite media swiss army tool ffmpeg:
for file in *.m4a; { ffmpeg -i "$file" -map_metadata -1 -c copy -y "$file"-stripped.m4a; } This little on-liner will create a copy of each m4a file with the meta-data removed. You can then use something like MusicBrainz Picard to re-tag them with the proper meta-data sans the purchased information. I think I know how to do a more surgical approach, and I will add that if I can figure the syntax out.
As far as I can tell, the relevant tags that need to be removed are:
purchase_date : 2020-01-01 11:04:44
account_id : someaccount@somedomain.comHowever, I do not see these tags in Picard.