docs: document /healthz endpoint and add Docker healthcheck

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

Author: koki-develop

README.md

@@ -102,6 +102,16 @@ $ docker compose up
 
 ### API
 
+#### `GET /healthz`
+
+Returns the service health status. Intended for load balancer health checks, Docker health checks, and Kubernetes liveness probes.
+
+Response:
+
+```json
+{"status":"ok"}
+```
+
 #### `POST /v1/run`
 
 Request:

compose.yml

@@ -9,3 +9,9 @@ services:
     command: ["serve", "--run-timeout", "10", "--compile-timeout", "10"]
     ports:
       - "8080:8080"
+    healthcheck:
+      test: ["CMD", "curl", "--fail", "http://localhost:8080/healthz"]
+      interval: 10s
+      timeout: 5s
+      retries: 3
+      start_period: 5s