chore: Add Docker build to CI (#11)

.github/workflows/ci.yml

@@ -21,3 +21,24 @@ jobs:
           cache: npm
       - run: npm ci
       - run: npm run lint
+
+  build:
+    name: Build
+    runs-on: ubuntu-latest
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up Docker Buildx
+        uses: docker/setup-buildx-action@v3
+
+      - name: Build
+        id: docker-build
+        uses: docker/build-push-action@v6
+        with:
+          context: ./
+          file: ./client/Dockerfile
+          platforms: linux/amd64,linux/arm64
+          push: false
+          cache-from: type=gha
+          cache-to: type=gha,mode=max