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/migrations/0020_typical_daimon_hellstrom.sql

@@ -0,0 +1,7 @@
+-- Clean up existing duplicate services before adding unique constraint.
+-- Keep the row with the lowest id per name; delete all others.
+DELETE FROM services WHERE id NOT IN (
+  SELECT (MIN(id::text))::uuid FROM services GROUP BY name
+);
+
+ALTER TABLE "services" ADD CONSTRAINT "services_name_unique" UNIQUE("name");