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/src/modules/db/db.routes.ts

@@ -0,0 +1,13 @@
+import type { FastifyPluginAsync } from 'fastify';
+
+export const dbRoutes: FastifyPluginAsync = async (fastify) => {
+  fastify.get('/db/health', async (_request, reply) => {
+    try {
+      await fastify.prisma.$queryRaw`SELECT 1`;
+      return { status: 'ok', database: 'reachable' };
+    } catch (err) {
+      fastify.log.error({ err }, 'database health check failed');
+      return reply.code(503).send({ status: 'error', database: 'unreachable' });
+    }
+  });
+};