Support Google login that links to existing accounts by email.
When a user who registered via email OTP signs in with Google using
the same email, they are linked to the same account.
Backend:
- Add POST /auth/google endpoint that exchanges Google auth code for
tokens, fetches user profile, and calls findOrCreateUser()
- Updates user name and avatar from Google profile on first Google login
Frontend:
- Add "Continue with Google" button on login page (shown when
NEXT_PUBLIC_GOOGLE_CLIENT_ID is configured)
- Add /auth/callback page to handle Google OAuth redirect
- Add loginWithGoogle to auth store and API client
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