I'm sorry to hear you're having the same issue. At least you're not alone in your frustration. If you haven't already, you should open a developer support ticket so they know multiple people are having the issue. If they have two accounts with the same problem that they can examine it may reveal a common core issue. To open the ticket I used my alternate Apple ID and went to developer.apple.com -> Contact Us -> Membership and Account -> Account Access -> 'Request Callback'. After you talk to the support rep and get a case number you'll get an email back saying that to communicate further with the support rep you'll have to login with the same ID that you're having the issue with, which of course you can't--but don't worry, their system does also route email replies to the support rep, so I've been able to talk to him over email and send additional information. It was escalated to engineering and they had me record Safari debug logs. The issue occurs though for any browser and device that I try, and I've tried a lot, so I doubt it's a browser issue. Do you use one Apple ID to log in to your computer and to make personal purchases and another one for app development, or do you normally just use one Apple ID for everything? I use separate personal and work Apple IDs but the problem occurs even if the device is logged into iCloud using the same ID that I'm trying to login to developer.apple.com with. So I don't think having separate IDs is this issue, but I was just curious if you use a similar setup. I've used this setup to develop apps for 14 years and everything has worked fine up until 2 days ago. I'll post anything else that I learn.

I'm still waiting for engineering to resolve the issue but I've uncovered some more potential clues. To access these forums I had to use a different Apple ID than the dev ID that's been having this issue. But I found that even this other Apple ID also has the same issue, but only if I manually type in the password or let the browser use auto-fill--and again, I know it's the correct password because a password failure results in a different error saying that the id or password is incorrect. Regardless of what browser or device I use, entering my credentials doesn't work. The only way I'm able to log in to any Apple website, on any device, with any ID, is if I use the Touch ID automatic login (I'm not referring to when Touch ID just auto-fills the password field, but the larger Touch ID dialog with the red thumb-print that automatically submits both username and password at the same time). As long as the Apple ID that Touch ID defaults to is the one I want to sign in with it works--but if I need click "Use a different Apple ID" in the Touch ID dialog it switches to manual form entry which results in the error. And unfortunately, the Touch ID dialog never defaults to the Apple ID I use for development. Touch ID could be working because it bypasses 2FA, and 2FA could be the core issue.

Okay, I made some incremental progress. After seeing that my personal Apple ID had the same issue and could not log in with username/password, but could login using Touch ID I tried logging into my laptop using my dev Apple ID and then signing into to App Store Connect, but that failed. (When I refer to Touch ID login I'm referring to the larger Touch ID window, not the one that just fills in the password because that fails). So then I decided to go buy another MacBook and set it up using my dev Apple ID. Then when I went to appstoreconnect.apple.com I was able to sign in using Touch ID. It's only a temporary solution because I don't want to spend $2k just to be able to manage my apps, so I do eventually want to return the laptop. Something in the 2FA backend seems to have changed because I've used separate Apple IDs for personal and dev work for 14 years with no issues. If you search online you only see App Developers reporting the issue because I think we're more likely to use multiple Apple IDs in order to separate personal and business purchases for tax purposes. But developers and support techs at Apple never see this because they probably just use one Apple ID. If you need to take the drastic step of buying another MacBook to access your dev account, Best Buy, has a good sale on M1 Macs and if you get TotalTech, which includes AppleCare, it extends your return window to 60 days.