feat(api): integrate Prisma client with /db/health endpoint

- Add @ketopath/db and fastify-plugin to apps/api
- prismaPlugin decorates the Fastify instance with prisma and disconnects
  on app close, with FastifyInstance type augmented in src/types/fastify.d.ts
- DATABASE_URL is now required by env validation
- New module modules/db with GET /db/health running SELECT 1 via Prisma
- dev script switched to tsx --env-file=.env for env loading

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

apps/api/package.json

@@ -4,7 +4,7 @@
   "private": true,
   "type": "module",
   "scripts": {
-    "dev": "tsx watch src/server.ts",
+    "dev": "tsx watch --env-file=.env src/server.ts",
     "build": "tsc",
     "start": "node dist/server.js",
     "typecheck": "tsc --noEmit",
@@ -15,8 +15,10 @@
     "@fastify/helmet": "^11.1.1",
     "@fastify/rate-limit": "^9.1.0",
     "@fastify/sensible": "^5.6.0",
+    "@ketopath/db": "workspace:*",
     "@ketopath/shared": "workspace:*",
     "fastify": "^4.28.1",
+    "fastify-plugin": "^4.5.1",
     "zod": "^3.23.8"
   },
   "devDependencies": {