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/0012_pet_photo.sql

@@ -0,0 +1,5 @@
+-- Add photo storage columns to pets table
+-- Ref: GitHub #93
+
+ALTER TABLE "pets" ADD COLUMN "photo_key" text;--> statement-breakpoint
+ALTER TABLE "pets" ADD COLUMN "photo_uploaded_at" timestamp;