MacBook Pro identity verification fails for iCloud/Messages

"Your identity couldn't be verified. Check your network connection or try again."

I just got my MBP back from the Genius Bar 3 days ago where they replaced the top case (keyboard, battery, Touch ID sensor, etc).

No issues Saturday, Sunday, Monday. Today though? Keep getting the above when trying to use iCloud/Messages. I now can't use Messages or most iCloud services on my Mac. My password is 100% correct. I've used it to (today) log into iCloud.com, and verify on my phone. Only doesn't work on my Mac.

I've tried restarting, changing my DNS from Cloudflare to Google, disconnecting/reconnecting wifi. I can't get it to accept my password. Even reset my Apple Account password. Again verified with new pw I can still login to iCloud.com...

Help?