Syncing new albums from Bandcamp to iPhone's music library via Apple Music app

So I just switched from a 13 pro max to a 16 pro max, and up until now I’d been using iTunes to load music from all kinds of sources onto my phones music library. I purchase and buy a lot from Bandcamp and don’t plan on getting Apple Music subscription cause I don’t like music streaming services.

ive been trying to put this new album I bought on Bandcamp but when I connect my phone to my pc’s Apple Music app, nothing happens. Does it work like iTunes and you gotta click a sync button? If so why is there no sync option? Like I’m lost here, legit need help pls.

[Re-Titled by Moderator]