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/0027_refunds.sql

@@ -0,0 +1,11 @@
+CREATE TABLE "refunds" (
+  "id" uuid PRIMARY KEY DEFAULT gen_random_uuid(),
+  "invoice_id" uuid NOT NULL REFERENCES "invoices"("id") ON DELETE RESTRICT,
+  "stripe_refund_id" text NOT NULL,
+  "idempotency_key" text UNIQUE,
+  "amount_cents" integer,
+  "created_at" timestamp NOT NULL DEFAULT NOW()
+);
+
+CREATE INDEX "idx_refunds_invoice_id" ON "refunds"("invoice_id");
+CREATE INDEX "idx_refunds_idempotency_key" ON "refunds"("idempotency_key");