fix(auth): log /health 503 error and surface message in body (CAR-1276)

The /health handler's catch block was empty, so when the DB probe
failed we had no log line to diagnose from. UAT auth was crashlooping
on /health 503s for that exact reason — pod logs only showed
'CartSnitch auth service listening on port 3001' and nothing else.

Add console.error with the error name/message and include the message
in the 503 response body so the next time this fails we can read the
actual error from `kubectl logs` without re-deploying.

This is the dev-side observability half of CAR-1276. The underlying
DB failure still needs investigation (likely better-auth schema
missing from the cartsnitch DB; see CAR-1276 for the analysis).

Tests updated to assert the new error field is present and a string.
Co-Authored-By: Paperclip <noreply@paperclip.ing>

auth/src/index.ts

@@ -21,9 +21,19 @@ const server = createServer(async (req, res) => {
       }
       res.writeHead(200, { "Content-Type": "application/json" });
       res.end(JSON.stringify({ status: "ok", db: "reachable" }));
-    } catch {
+    } catch (err) {
+      // Log the actual error so /health 503s are diagnosable from pod logs
+      // (CAR-1276: UAT auth was crashlooping with no log output beyond the
+      // initial "listening on port 3001" line because this catch was empty).
+      console.error(
+        "[auth /health] DB probe failed:",
+        err instanceof Error ? `${err.name}: ${err.message}` : err,
+      );
+      const detail = err instanceof Error ? err.message : "unknown error";
       res.writeHead(503, { "Content-Type": "application/json" });
-      res.end(JSON.stringify({ status: "error", db: "unreachable" }));
+      res.end(
+        JSON.stringify({ status: "error", db: "unreachable", error: detail }),
+      );
     }
     return;
   }