Extract groombook/api from monorepo with CI workflow

- Add source code from apps/api
- Add packages/db and packages/types workspace dependencies
- Add GitHub Actions CI workflow (lint, typecheck, test, docker)
- Generate pnpm-lock.yaml
- Add .gitignore

Co-Authored-By: Paperclip <noreply@paperclip.ing>

packages/db/migrations/0008_business_settings.sql

@@ -0,0 +1,15 @@
+CREATE TABLE IF NOT EXISTS "business_settings" (
+  "id" uuid PRIMARY KEY DEFAULT gen_random_uuid() NOT NULL,
+  "business_name" text DEFAULT 'GroomBook' NOT NULL,
+  "logo_base64" text,
+  "logo_mime_type" text,
+  "primary_color" text DEFAULT '#4f8a6f' NOT NULL,
+  "accent_color" text DEFAULT '#8b7355' NOT NULL,
+  "created_at" timestamp DEFAULT now() NOT NULL,
+  "updated_at" timestamp DEFAULT now() NOT NULL
+);
+
+-- Seed a default row so GET always returns something
+INSERT INTO "business_settings" ("business_name", "primary_color", "accent_color")
+VALUES ('GroomBook', '#4f8a6f', '#8b7355')
+ON CONFLICT DO NOTHING;