feat: Sprint 1 remainder — Postgres store, Docker client, warm pool, sessions route

- PostgresUserStore (Queryable) + migration + env-gated wiring
- DockerodeClient behind injected DockerEngine
- ImageManager, WarmPool, Dockerfile.wordpress, docker-compose
- POST /sessions spins up sandbox (503 when unconfigured)
- ADRs 0014-0015; 68 unit tests green

api/package.json

@@ -8,10 +8,14 @@
     "start": "tsx src/index.ts"
   },
   "dependencies": {
-    "fastify": "^5.2.0"
+    "dockerode": "^5.0.1",
+    "fastify": "^5.2.0",
+    "pg": "^8.23.0"
   },
   "devDependencies": {
+    "@types/dockerode": "^4.0.1",
     "@types/node": "^22.10.0",
+    "@types/pg": "^8.21.0",
     "tsx": "^4.20.3",
     "typescript": "^5.9.2",
     "vitest": "^3.2.4"