test(e2e): add Cypress scaffold + CI job

.github/workflows/ci.yml

@@ -83,3 +83,32 @@ jobs:
           path: |
             backend/coverage.xml
             frontend/coverage/**
+
+  e2e:
+    runs-on: ubuntu-latest
+    needs: [check]
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v4
+
+      - name: Set up Node
+        uses: actions/setup-node@v4
+        with:
+          node-version: "20"
+          cache: npm
+          cache-dependency-path: frontend/package-lock.json
+
+      - name: Cypress run
+        uses: cypress-io/github-action@v6
+        with:
+          working-directory: frontend
+          install-command: npm ci
+          build: npm run build
+          start: npm start
+          wait-on: http://localhost:3000
+          command: npm run e2e
+        env:
+          NEXT_TELEMETRY_DISABLED: "1"
+          # Force Clerk disabled in E2E to keep tests secretless/deterministic.
+          NEXT_PUBLIC_CLERK_PUBLISHABLE_KEY: ""