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>

.github/workflows/ci.yml

@@ -77,11 +77,8 @@ jobs:
       - name: Install dependencies
         run: pnpm install --frozen-lockfile
 
-      - name: Build packages
-        run: |
-          pnpm --filter @groombook/types build
-          pnpm --filter @groombook/db build
-          pnpm --filter @groombook/api build
+      - name: Build
+        run: pnpm --filter @groombook/api build
 
   docker:
     name: Build & Push Docker Images