Initial extraction: groombook/api from groombook/app monorepo

Part of GRO-802 monorepo breakdown.

Changes:
- Extract apps/api/ as the main API service
- Inline packages/db/ (database schema, migrations, utilities)
- Inline packages/types/ (shared TypeScript types)
- Add CI workflow for lint, typecheck, test, build, docker
- Port Dockerfile with 4 stages: runner, migrate, seed, reset

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

packages/db/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");