I have almost the exact same issue. My account used to be on a one card, which I cancelled. I've updated my Claude subscription to another one and worked without any issues including MFA/OTP.

For some reason I really don't understand, it's a different payment process in the on the Developer Platform page. When I tried to update there with 3 different credit cards (MC, Visa, AmEx) and using Stripe Link, they all got the same rejection. It's clearly some bug / issue on their side.

Their chat bot is honestly an embarrassment for a frontier AI company like Anthropic, generic, not helpful and trying to lecture me on what MFA/OTP implicating "it's you being to stupid to use a credit card".

I'm also waiting already for 2 weeks for a human support on my 2 messages.

This whole thread shows I am (and you are) not alone with this issue, so it's hard to understand how the "engineering team checked" and didn't find anything.

I've been building payments systems for over a decade and just projecting from this thread their support should be blowing up from such an issue - I know in my companies it would have.