add nuxt typecheck and build github CI

.github/workflows/ci.yml

@@ -0,0 +1,31 @@
+name: CI
+
+on:
+  push:
+    branches:
+      - main
+  pull_request:
+
+jobs:
+  build:
+    name: Typecheck and Build Nuxt App
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+
+      - name: Setup Node.js and pnpm
+        uses: actions/setup-node@v4
+        with:
+          node-version: 20
+          cache: "pnpm"
+
+      - name: Install dependencies
+        run: pnpm install
+
+      - name: Typecheck
+        run: pnpm nuxt typecheck
+
+      - name: Build
+        run: pnpm nuxt build