Why is Apple Music not connecting on my MacBook Pro?

When I launch the Apple Music App (on an Intel MacBook Pro 11.3 running Big Sur 11.7.10), I suddenly cannot connect to Apple Music (i.e. the Listen Now, Browse and Radio options).

I've tried: to logout then log back in to my Apple account (no change); check my subscription is current (it is); my Apple Music subscription works on my iPhone; my Mac is authorised; turning NetBarrier or VirusBarrier (both from Intego) off makes no difference; restarting the Apple Music app or the Mac makes no difference; Apple Music preferences seem appropriate; my internet connection is fine.

Interestingly, I can access the iTunes Store from within the Apple Music app.

Any suggestions would be very welcome!

[Re-Titled by Moderator]