Based on some recent experience maintaining a public-facing website, I would
figure out if the spammers are actually getting anything useful. If not,
they're probably just probing for a weakness and will quit in a few
hours (or maybe days) when they learn there's nothing to be gained. This happened to me on a few occasions. Also, if all the requests are coming from the same IP, you could block that IP for a week and they'll probably quit.
However, I will also volunteer this:
I've recently been working with AWS Cognito and it might be another option. It supports signing up with an email address which Cognito will verify (when configured to do so). The AWS free tier includes up to 50,000 monthly active users.
Cognito also allows people to log in with Facebook/Google/Apple/Amazon, and adding Github would probably be pretty easy. I haven't personally gotten this far yet, but I think these users are also included in the 50,000 free tier limit.
In about a month, I should have time to work on this if it sounds viable and desirable to whomever would make that decision.