Is it letting you play through MacBook speakers ok? Or is this just when you try to use the HomePods? Can you play Apple Music from other devices? Is your Apple Music subscription active?
On your Mac while in the music app, at the top Account - sign out then sign back in. in case it’s your MacBook Account.
- I should mention also you can look in HomePod settings also in the home app. Long press or right click to bring up settings - Primary User to check you’re signed in. If signed in, sign out, then sign back in.
- Use the same Apple ID you’re using for Apple Music, preferably you should use the same ID for everything Apple.
- in iCloud- keychain should be enabled - on all devices