Add web CI (#473)

.github/workflows/web.yaml

@@ -0,0 +1,31 @@
+name: Web CI
+
+on:
+  push:
+    branches: [ main ]
+    paths:
+      - '.github/**'
+      - 'web/**'
+  pull_request:
+    paths:
+      - '.github/**'
+      - 'web/**'
+
+jobs:
+  test:
+    runs-on: ubuntu-latest
+    defaults:
+      run:
+        working-directory: web
+
+    steps:
+      - uses: actions/checkout@v5
+
+      - uses: actions/setup-node@v4
+        with:
+          node-version: '22'
+
+      - run: npm install
+      - run: npm run check
+        continue-on-error: true
+      - run: npm run test:unit