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/0023_auth_provider_config.sql

@@ -0,0 +1,14 @@
+CREATE TABLE "auth_provider_config" (
+	"id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+	"provider_id" text NOT NULL,
+	"display_name" text NOT NULL,
+	"issuer_url" text NOT NULL,
+	"internal_base_url" text,
+	"client_id" text NOT NULL,
+	"client_secret" text NOT NULL,
+	"scopes" text DEFAULT 'openid profile email' NOT NULL,
+	"enabled" boolean DEFAULT true NOT NULL,
+	"created_at" timestamp DEFAULT now() NOT NULL,
+	"updated_at" timestamp DEFAULT now() NOT NULL,
+	CONSTRAINT "auth_provider_config_provider_id_unique" UNIQUE("provider_id")
+);