am I permanently barred from YA?

No, you're not. Just don't give them the number and keep on going.

Every legitimate website will tell you that it is not their policy to ask for such information.  If someone does ask, claiming to be Yahoo, they are fakers trying a "phishing" scam.  Ignore them.

You better get used to the idea of not using the internet then, as gradually all major sites are (or will be) moving over to requiring proof of identity to cut down on spammers, trolls and abuse of many types.

The laws in various countries are being made much stricter and site owners may be prosecuted if they do not properly "police" their sites to combat abuse and such as copyright violations.

You are being asked for just a phone number - Facebook already demand a photo ID, driving licence or passport, if they suspect anything dubious...

If you were banned you wouldn't be able to post here. You can't sign up for an account unless you supply a mobile number. Info required to create a Yahoo account: https://help.yahoo.com/kb/mail-for-desktop/info-re...

All part of their security. They will ask for alternative ways of contacting you for a while, then they will lock you out. Only way to get back in is with the info you provided them. If you don't provide any or have outdated info. You're done on Ya.