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/0003_recurring_series.sql

@@ -0,0 +1,10 @@
+-- Add recurring_series table to store recurrence patterns
+CREATE TABLE "recurring_series" (
+	"id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+	"frequency_weeks" integer NOT NULL,
+	"created_at" timestamp DEFAULT now() NOT NULL
+);
+
+-- Extend appointments with series tracking
+ALTER TABLE "appointments" ADD COLUMN "series_id" uuid REFERENCES "recurring_series"("id") ON DELETE SET NULL;
+ALTER TABLE "appointments" ADD COLUMN "series_index" integer;