Came across this today, figured I check it out.
I have been able to reproduce the problem, so I got on the blower with Apple.
Got through to some guy, told him that I was running the latest Big Sur beta and he connected to my machine through the share screen software built into macOS. He saw that the "Listen Now" view on the Music app, and in both "beta." and "music." apple.com the same issue was present.
Another member of the household, also running Big Sur had the same problem.
I was transferred to a Senior Advisor who's demeanour was that she was only speaking to me to compile a bug report for Apple's engineers, refused to connect to my machine to view the issue because it was "Beta". Gave them a Windows VM which they reproduced all the issues on through screen sharing. And, a Catalina VM which they too reproduced the issue on.
Anyhow, I'm expecting a call back, the case has been reported to someone at least.
While they twiddle their thumbs, I looked into this further. The web version, "music.apple.com" is returning an error when requesting "recommendations", it has something to do with a javascript file passing a timezone incorrectly, and Apple are then returning a "Your timezone is invalid" error: the timezone being passed to Apple is '00:00', someone clearly had not consumed enough coffee when they pushed that code...
Apple needs to find new testers 👍🏻