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/__tests__/health.test.ts

@@ -19,9 +19,18 @@ describe('Auth health endpoint', () => {
             }
             res.writeHead(200, { 'Content-Type': 'application/json' });
             res.end(JSON.stringify({ status: 'ok', db: 'reachable' }));
-          } catch {
+          } catch (err) {
+            // Mirror src/index.ts: log the error and include the message in the
+            // response body so /health 503s are diagnosable from pod logs.
+            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;
         }
@@ -76,7 +85,10 @@ describe('Auth health endpoint', () => {
     close();
 
     equal(status, 503);
-    equal(body, '{"status":"error","db":"unreachable"}');
+    const parsed = JSON.parse(body);
+    equal(parsed.status, 'error');
+    equal(parsed.db, 'unreachable');
+    equal(parsed.error, 'connection refused');
   });
 
   it('returns 503 with db=unreachable when query times out', async () => {
@@ -95,7 +107,14 @@ describe('Auth health endpoint', () => {
     close();
 
     equal(status, 503);
-    equal(body, '{"status":"error","db":"unreachable"}');
+    const parsed = JSON.parse(body);
+    equal(parsed.status, 'error');
+    equal(parsed.db, 'unreachable');
+    // The query promise rejects with a synthetic 'timeout' error; the
+    // Promise.race wrapper also rejects with 'DB timeout'. The body should
+    // surface whichever error was thrown — accept either to stay robust.
+    equal(typeof parsed.error, 'string');
+    equal(parsed.error.length > 0, true);
   });
 
   it('returns a terminal response for unknown paths (no hang)', async () => {