Losing your email isn't DigitalOcean's fault and the fact that they are actively working on getting you access back should prevent you from naming and shaming them.
I do think it's at least surprising that changing your email address on GitHub would cause you to lose access to places where you used GitHub 3rd party auth to login. If those schemes don't centralize management of those kinds of details to the auth provider, what's the point of them?
I love Digital Ocean, don't get me wrong.
Im just sharing the Bad experience with the "Social Authentication" flow and how long it is taking to solve a simple problem.
This also a heads up for anyone using GitHub as the authentication method.
It's definitely not a simple problem though. Anyone can claim they own your account. And it would be bone-headed to make the re-verification process easy.
If he is using github account, all he need is to authenticate with it. He is not obliged to keep his email, phone, home address and authenticator ready because system deciding he is sus every 30 days.