I was having the same issue for both accounts: personal and work (different Apple IDs).
After unsuccessful attempts to login, change networks (wi-fi, cellular, vpn), etc.
I've contacted apple support via the Apple Support app on iOS and we scheduled a call:
I was asked to attempt logging into appleid.apple.com instead of a developer.apple.com. It somehow worked.
Then I was walked through the process of resetting Apple ID password. It can be done either from appleid.apple.com if you were able to access it or using a logged in iOS device.
I did reset password for both: personal and work Apple IDs.
After that I was able to log in into both of my developer accounts.