Apple ID locked, can't unlock or change password

Hi. I'm writing from my wife's ID because my own is locked. It was locked after I have removed an old device from the devices list on my iPhone 13 with iOS 17 and tried to register a new device after that.

I tried to follow unlock steps but the process freezed and failed most of the times on Unlock stage or it did go through unlock (after reboot mostly), asked for my phone number and gave me to chose one of my numbers to send me a code, accepted the code and asked for ID password again but gave me the server error and did not go further. I tried to go through all process on appleid site with the same result with unknown error and in support app on my friend's iPhone i tried to change password but got the same error or a request for 28-symbol recovery code which I didn't write down and now it's on my iPhone where I've logged in but Apple ID does not work so I can't look for this code and can't change password, finish restoration with all my password, pin and my own face or even log out.

The same error I get when trying to change password on Apple's web page and when trying to unlock ID or change it's password on new device.

It will be sad to lose ID with all it's purchases and subscriptions and my huge Apple Music library with hundreds of tracks with customized tags.