How new your Mac is doesn't affect that. The only reason that I know of for the Deauthorize All button not displaying as described in my original post is the following from those instructions:
If you haven't authorized 2 or more computers, you won't see this section.
If you are using the Music app on your new Mac and following the instructions below exactly and if "Computer Authorizations" in the screenshot below shows more than 1 authorized computer and there is no Deauthorize All button to the right of that, contact Apple Support to see if they can help. There is a Get Support link at the top right of this page.
To automatically sign in to your Account Information page from your computer, click here. Or follow these steps:
- On a Mac, open the Music app, Apple TV app, or Apple Books app. On a PC, open iTunes for Windows.
- Sign in with your Apple ID.
- In the menu bar on your Mac or PC, choose Account > View My Account.
- Sign in with your Apple ID.
- On the Account Information page, scroll to the Apple ID Summary section. You'll see the number of computers that you've authorized with your Apple ID. You can’t see the names of those computers. If you haven't authorized 2 or more computers, you won't see this section.