Music is authorized but still wont play songs

Repeated requests to authorize an already authorized computer for store downloads typically indicates you have corrupt or incomplete copies. Backup and then delete the tracks that won't play from your library without hiding from your purchase history. Redownload using the cloud links that should remain, or close iTunes and reopen if they don't show up straight away. While downloading click the activity widget and turn off the option that allows for simultaneous downloads.

tt2

Hmm, there are two security mechanisms connected to iTunes/Apple Music content. When you say "I only have 2 devices on my account" you might be looking at the wrong one. See Authorization vs. association - Apple Community. If your computer is already authorized to your Apple ID it may help to deauthorize and then reauthorize it.

tt2

Ordinarily playing purchased (unprotected) songs doesn't cause there to be any message about authorization. A message that you might need to authorize is correctly associated with pre-2010 purchases when your computer isn't authorized, or incorrectly with corrupted downloads that, for reasons unknown, aren't properly unpacked after download. An assumption is they they might be encrypted in some fashion for delivery to your computer and are supposed to be decrypted on arrival. Do a full power cycle of your router and computer to rule out odd gremlins. Hold down option+cmd as you launch Music to open it in its Safe Mode.

Do you have the Apple Music service in addition to the app? Catalina and later use Music rather than iTunes for music playback, and Finder to manage devices unless you're doing that through the cloud.

tt2

Not wrong computer, wrong mechanism. You can see a list of associated devices. There is no list of authorized computers. What happens when you try to play other content from your library? Is there an error message? Do tracks gain an exclamation mark after failing to play?

tt2