Restore production Google OAuth start flow

[sarthakagrawal927]

Observed

A no-cookie POST to https://rolepatch.com/api/auth/sign-in/social with provider: google returns HTTP 500 and no Google authorization URL. GET /api/auth/get-session remains healthy (HTTP 200), so the failure is isolated to the Google provider path.

Likely cause

src/lib/auth.ts registers the Google provider only when both GOOGLE_CLIENT_ID and GOOGLE_CLIENT_SECRET are present in the production runtime. The deployed runtime therefore needs its Google OAuth credentials and Better Auth URL/trusted-origin values verified.

Acceptance criteria

• The production social-sign-in endpoint returns a Google authorization URL for a no-cookie request.
• A real Google sign-in returns to the requested in-product callback.
• Do not expose credential values in code, logs, or the issue.