How signing in works, and what it does and doesn't give you.
RG AI uses Firebase Authentication (Google infrastructure) for sign-in. RG AI never sees or stores your password - Google/GitHub handle that entirely.
There is currently no email/password sign-in and no other social providers. If you signed up with Google, use Google again to log back in - the two aren't interchangeable.
Note: Chat itself works without signing in - an account mainly exists to keep your history and let you connect a key.