I have problem since 4-5 Dec. Had 2 chats with the support - on first they suggested to wait 24hrs, on the second they suggested to make the call with the support. On the call (already 9th Dec, had no access for 4 days) they suggested to initiate password reset procedure and use another phone (even when I know password, has my mail and phone working). On next day I receive email that says I should wait until 23Dec to "receive a text or phone call at this number when your account is ready to recover", whatever it means... Never made this procedure so I don't know what to expect.
In any case I'm sure that the problem on the Apple's side because I know few people who faced the same problem at the same time period plus some amount of posts on the Internet.
@aizirek112, you can try to create new account with iCloud mail like suggested in this reddit comment. In my case it will not help as I need to login to the old one...
P.S. Have my work account blocked, right now using personal via passkey verification to post tis message. Phone verification is broken.