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/0022_logo_key.sql

@@ -0,0 +1,2 @@
+-- Add logo_key column to business_settings for S3-based logo storage
+ALTER TABLE "business_settings" ADD COLUMN "logo_key" text;