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/types/package.json

@@ -0,0 +1,22 @@
+{
+  "name": "@groombook/types",
+  "version": "0.0.1",
+  "private": true,
+  "type": "module",
+  "main": "./dist/index.js",
+  "types": "./src/index.ts",
+  "exports": {
+    ".": {
+      "default": "./dist/index.js",
+      "types": "./src/index.ts"
+    }
+  },
+  "scripts": {
+    "build": "tsc",
+    "typecheck": "tsc --noEmit"
+  },
+  "devDependencies": {
+    "typescript": "^5.7.3"
+  },
+  "license": "AGPL-3.0-only"
+}