After trying many many times over several HOURS, the bottom area that says "Having problems?" added an option for "Use GitHub Mobile" which was NEVER there before in every single attempt I made before going back for several hours. I clicked it, a number was shown, and I entered the number on my old phone.

Issue is resolved. By far the worst 2fa experience of my life, and not even close, and I know I'd be completely locked out without my old phone.