Verification failed. Unknown error occured. After migration to new MacBook Pro.

When setting up iCloud, I get "Verification failed. Unknown error occurred" on my brand new Macbook pro that was migrated from my old Macbook pro (2011) last night.

With the same Apple ID and password I was able to log in to appleid.apple.com and wwww.icloud.com. I only have one Apple ID. If I give wrong password, I get username or password is incorrect (or similar).

So far I have tried to following and nothing works, just "Verification failed":

• Restart new laptop, retry to give Apple ID password to iCloud prompt at the top of settings.
• Log out of iCloud (it was remembering my email from migration), restarted laptop, tried to login to iCloud in settings, after this settings didn't remember my email, so had completely rejected the login.
• Changed Apple ID password on my phone, restarted laptop, tried to login to icloud in settings, this gave two factor authentication message in phone, but after giving the numbers on laptop I got the same error message. After this settings did remember my email for iCloud.
• Went to www.icloud.com and removed my new laptop from Device list, restarted laptop, tried to login to iCloud in settings.
• Started my old laptop and signed out of iCloud there.
• Restarted my new laptop, tried to login to iCloud in settings.

Now I have run out of ideas what to try.

PS. As a software professional I loathe to get "Unknown error occurred", it does not help in getting the thing sorted out.