I'm having exactly the same problem as you, and your post perfectly describes what I'm experiencing:

First attempt to log in via Google => error "State cookie was missing".

Second attempt (with the exact same email) => it goes through without a hitch.

Onsite, everything works perfectly; it only fails in production. (I also sometimes get a "PKCE code_verifier cookie missing" error with Apple in production, which I can't reproduce locally or in production - only certain users are affected.)

Have you found a solution since your post? If so, I'd be super interested! Thanks in advance.