iTunes Match

Apple Music is essentially an extension to iTunes Match allowing not only your existing media and playlists to be added to a cloud library, but also anything else you fancy from the Apple Music catalog while your subscription remains active. You don't need both services. If you've purchased the subscription to iTunes Match you should have an option to turn on sync library. I see more options on that tab than you show in your screenshot. Try signing out of your Apple ID and then sign in again using the Account menu in Music.

If you still cannot get it to work reach out to Official Apple Support.

tt2

Are you signed into your Apple ID, and is your computer authorized to your Apple ID? This looks like the Music app in Catalina or later rather than iTunes. Are you sure that your subscription to iTunes Match has been completed? See Use Sync Library to access your music library across your devices - Apple Support for details of how this control works in Music, i.e. the same as Apple Music. You should see a Sync Library option with your Apple ID mentioned.

tt2

Make sure that your computer is authorized.

See Authorize or deauthorize your computer for iTunes Store purchases - Apple Support

Check your account to see if the purchase was successful.

See https://reportaproblem.apple.com/ and/or Subscriptions and Billing - Official Apple Support.

tt2

Try iTunes > Preferences > General > iCloud Music Library. When this checkbox is ticked iTunes should scan your library matching or uploading your library to the cloud so that the same collection of music and playlists can be access from multiple computers or devices.

tt2

Glad to hear you got it all sorted. 🙂

tt2