@FediTips "sure" was a typo -= should have been "site" (I've now edited the original post - apologies for the confusion!)

As an example I use @openbenches which uses allows sign in (https://openbenches.org/add/logged_in) via auth0 to authenticate with a mastodon server. Hopefully that helps.

@FediTips
> If I've missed something let me know

I've never tried moving and I don't know the answer, but what would happen to any third party (non-mastodon) sure that you had an account on which used your Mastodon account for authentication? Would they redirect too? (I'm guessing that if your original server disappeared you'd be stuck in that case).
Possibly worth adding that into the questions at the end.