I bet if you sign out of iCloud then reinstall the Mac and sign in again it'll work again. This is probably the machine signing key being shot down for using it with an unauthorised client rather than the mac being completely banned itself.
Activation is tied to the Mac's serial number, so you either need to work with Apple Support to get your Mac's serial number off the blocklist, or you need to change your Mac's serial number to a unique and valid one that isn't blocked.
https://www.tonymacx86.com/threads/an-idiots-guide-to-imessa...
It’s important to note that an error in the former config could be ignored for like a month without any actual service disruption; it was 100% aesthetic in some cases.
A week ago I updated my beeper client and it set itself to automatically refresh registration tokens and got banned. I disabled iMessage on all my devices after that.
I won't abide a company punishing its users for wanting the convenience of picking up their text message convos from Linux because it's otherwise too distracting to pick up a phone each time.
Really happy to take one for the team. I mean that. This was going to happen at some point in the future whether or not I liked it, glad it happened now. I can't live in a world this connected where my linux box and 12 years of texting history is totally cut off from it. No thanks.