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/0009_client_soft_delete.sql

@@ -0,0 +1,6 @@
+-- Add client status (soft-delete support)
+CREATE TYPE "client_status" AS ENUM ('active', 'disabled');
+
+ALTER TABLE "clients"
+  ADD COLUMN "status" "client_status" NOT NULL DEFAULT 'active',
+  ADD COLUMN "disabled_at" timestamp;