Add CI Docker build verification job in main CI workflow (#407)

Author: Copilot

.github/workflows/ci.yml

@@ -10,6 +10,9 @@ on:
       - gh-pages
       - main
 
+permissions:
+  contents: read
+
 jobs:
   lint-and-test:
     runs-on: ubuntu-latest
@@ -39,3 +42,13 @@ jobs:
 
       - name: Run tests
         run: npm test
+
+  docker-build-check:
+    runs-on: ubuntu-latest
+
+    steps:
+      - name: Checkout code
+        uses: actions/checkout@v4
+
+      - name: Build Docker image
+        run: docker build -f docker/Dockerfile .