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/src/__tests__/petPhotos.test.ts

@@ -40,7 +40,7 @@ function resetDb() {
 
 // ─── Module mocks ─────────────────────────────────────────────────────────────
 
-vi.mock("./packages/db", () => {
+vi.mock("./db", () => {
   const pets = new Proxy(
     { _name: "pets" },
     { get(t, p) { return p === "_name" ? "pets" : {}; } }