If you run into a problem logging in manually with a username/password on iPhone, iPad, or Mac, this is most likely due to a strange OS bug which can prevent the form from working.
Simply restarting your device should fix the problem.
If that doesn’t fix things for you, you can use Sign in with Apple to create a second account (skip adding cards or upgrading), then use the Contact the Developer button in the app’s Settings to send your new account identifier, which can then be used to merge the two accounts.