feat(api): add DB-touching /api/readyz so schema loss cannot hide behind /health (GRO-2678)

- Register GET /api/readyz after /api/health in src/index.ts (before authMiddleware)
- Runs `getDb().select({id: staff.id}).from(staff).limit(1)` inside try/catch
- Success → 200 {"status":"ready"}; failure → 503 {"status":"degraded","check":"db"}
- Raw driver error is console.error'd but never leaked to the response body
- /health and /api/health are unchanged (K8s probes remain DB-less per CTO decision)
- New unit tests: mock getDb to resolve → assert 200/ready; throw → assert 503/degraded
- Updated UAT_PLAYBOOK.md §4.0 with TC-API-0.2 and TC-API-0.3

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

src/index.ts

@@ -65,6 +65,17 @@ app.use(
 app.get("/health", (c) => c.json({ status: "ok" }));
 // /api/health: used by Gateway HTTPRoute (/api/* → API pod)
 app.get("/api/health", (c) => c.json({ status: "ok" }));
+// /api/readyz: DB-touching deep health check consumed by monitoring (not K8s probes)
+// Distinct from /health so a dropped schema triggers an alert without cycling pods (GRO-2678)
+app.get("/api/readyz", async (c) => {
+  try {
+    await getDb().select({ id: staff.id }).from(staff).limit(1);
+    return c.json({ status: "ready" }, 200);
+  } catch (err) {
+    console.error("[readyz] DB check failed:", err);
+    return c.json({ status: "degraded", check: "db" }, 503);
+  }
+});
 
 // Public booking routes — no auth required, must be registered before auth middleware
 app.route("/api/book", bookRouter);