ci(playwright): Add Playwright E2E tests to CI workflow

This sets up the playwright tests the same way the existing integration tests are setup today to prove they can work well in CI.

Integrates the Playwright E2E test suite into the `code-qa.yml` CI workflow.
This new job, `playwright-e2e-test`, runs only if an `OPENROUTER_API_KEY`
secret is available, ensuring that the tests are executed in environments
where the necessary API key is provided.

Author: hassoncs

.github/workflows/code-qa.yml

@@ -90,9 +90,28 @@ jobs:
               working-directory: apps/vscode-e2e
               run: xvfb-run -a pnpm test:ci
 
+    playwright-e2e-test:
+        runs-on: ubuntu-latest
+        needs: [check-openrouter-api-key]
+        if: needs.check-openrouter-api-key.outputs.exists == 'true'
+        steps:
+            - name: Checkout code
+              uses: actions/checkout@v4
+            - name: Setup Node.js and pnpm
+              uses: ./.github/actions/setup-node-pnpm
+            - name: Install Playwright browsers
+              working-directory: apps/playwright-e2e
+              run: npx playwright install --with-deps
+            - name: Create .env.local file
+              working-directory: apps/playwright-e2e
+              run: echo "OPENROUTER_API_KEY=${{ secrets.OPENROUTER_API_KEY }}" > .env.local
+            - name: Run Playwright E2E tests
+              working-directory: apps/playwright-e2e
+              run: xvfb-run -a pnpm test:ci
+
     notify-slack-on-failure:
         runs-on: ubuntu-latest
-        needs: [check-translations, knip, compile, unit-test, integration-test]
+        needs: [check-translations, knip, compile, unit-test, integration-test, playwright-e2e-test]
         if: ${{ always() && github.event_name == 'push' && github.ref == 'refs/heads/main' && contains(needs.*.result, 'failure') }}
         steps:
             - name: Checkout code