fix(GRO-1544): restore /health alongside /api/health endpoint

The previous GRO-1544 PR changed /health to /api/health but removed
the /health endpoint entirely. This breaks:
- Dockerfile HEALTHCHECK (curl -f http://localhost:3000/health)
- K8s readinessProbe/livenessProbe (httpGet: path: /health, port: 3000)

Both paths are registered before auth middleware so both remain
publicly accessible without authentication.

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

UAT_PLAYBOOK.md

@@ -21,6 +21,14 @@ GroomBook API is a Hono-based REST service (TypeScript/Node.js) powering the pet
 
 ## Test Cases
 
+### 4.0 Health Check
+
+| # | Scenario | Steps | Expected |
+|---|----------|-------|----------|
+| TC-API-0.1 | Unauthenticated health check | GET /api/health | 200 OK, `{"status":"ok"}` |
+
+> **Note (GRO-1544):** Health endpoint registered on `api` basePath before auth middleware at `/api/health`. The old path `/health` was incorrect (routed to web pod via HTTPRoute `/*` rule).
+
 ### 4.1 Authentication
 
 | # | Scenario | Steps | Expected |

src/index.ts

@@ -58,8 +58,11 @@ app.use(
   })
 );
 
-// Health check (no auth required)
+// Health check — no auth required, registered on app at full path before auth middleware
+// /health: used by Dockerfile HEALTHCHECK and K8s readinessProbe/livenessProbe (port 3000 direct)
 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" }));
 
 // Public booking routes — no auth required, must be registered before auth middleware
 app.route("/api/book", bookRouter);