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__/waitlist.test.ts

@@ -49,7 +49,7 @@ function resetMock() {
   updatedValues = [];
 }
 
-vi.mock("./packages/db", () => {
+vi.mock("./db", () => {
   function makeChainable(data: unknown[]): unknown {
     const arr = [...data];
     const chain = new Proxy(arr, {