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/0004_reminder_logs.sql

@@ -0,0 +1,11 @@
+-- Add email opt-out flag to clients
+ALTER TABLE "clients" ADD COLUMN "email_opt_out" boolean NOT NULL DEFAULT false;
+
+-- Track sent reminders to prevent duplicate sends
+CREATE TABLE "reminder_logs" (
+	"id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+	"appointment_id" uuid NOT NULL REFERENCES "appointments"("id") ON DELETE CASCADE,
+	"reminder_type" text NOT NULL,
+	"sent_at" timestamp DEFAULT now() NOT NULL,
+	UNIQUE ("appointment_id", "reminder_type")
+);