fix(auth): add DB connectivity check to health endpoint

- Export pool from auth.ts for use in health check
- Replace static ok response with SELECT 1 query
- Return 503 with db=unreachable on failure or timeout

Co-Authored-By: Paperclip <noreply@paperclip.ing>

auth/src/index.ts

@@ -7,7 +7,6 @@ const port = parseInt(process.env.PORT ?? "3001", 10);
 const handler = toNodeHandler(auth);
 
 const server = createServer(async (req, res) => {
-  // Health check
   if (req.url === "/health" && req.method === "GET") {
     try {
       const client = await pool.connect();