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/0025_rate_limit.sql

@@ -0,0 +1,6 @@
+-- Better-Auth rate limiting table (GRO-574)
+CREATE TABLE "rate_limit" (
+  key TEXT NOT NULL PRIMARY KEY,
+  count INTEGER NOT NULL,
+  last_request BIGINT NOT NULL
+);