refactor: inline packages/db and packages/types into api package

Phase 2 extraction: groombook/api from groombook/app monorepo.

Changes:
- Move packages/db content to apps/api/src/db/
- Move packages/types content to apps/api/src/types/
- Inline database schema and migrations into api package
- Update Dockerfile to build single package
- Update CI workflow for single-package structure
- Fix vitest.config.ts aliases

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/package.json

@@ -9,22 +9,26 @@
     "start": "node dist/index.js",
     "lint": "eslint src --ext .ts",
     "typecheck": "tsc --noEmit",
-    "test": "vitest run"
+    "test": "vitest run",
+    "db:generate": "drizzle-kit generate",
+    "db:migrate": "drizzle-kit migrate",
+    "db:seed": "tsx src/db/seed.ts",
+    "db:reset": "tsx src/db/reset.ts && drizzle-kit migrate && tsx src/db/seed.ts",
+    "db:studio": "drizzle-kit studio"
   },
   "dependencies": {
     "@aws-sdk/client-s3": "^3.800.0",
     "@aws-sdk/s3-request-presigner": "^3.800.0",
-    "@groombook/db": "workspace:*",
-    "@groombook/types": "workspace:*",
     "@hono/node-server": "^1.13.7",
     "@hono/zod-validator": "^0.7.6",
     "better-auth": "^1.5.6",
+    "drizzle-orm": "^0.38.4",
     "hono": "^4.6.17",
     "node-cron": "^3.0.3",
     "nodemailer": "^6.9.16",
+    "postgres": "^3.4.5",
     "stripe": "^22.0.0",
     "telnyx": "^1.23.0",
-
     "zod": "^4.3.6"
   },
   "devDependencies": {
@@ -32,6 +36,7 @@
     "@types/node-cron": "^3.0.11",
     "@types/nodemailer": "^6.4.17",
     "@vitest/coverage-v8": "^3.2.4",
+    "drizzle-kit": "^0.30.4",
     "eslint": "^9.18.0",
     "tsx": "^4.19.2",
     "typescript": "^5.7.3",