fix: improve test infrastructure based on PR review

- Fix double build in CI: remove redundant build from playwright webServer
- Export chat helpers from shared module for proper unit testing
- Replace waitForTimeout with explicit waits in E2E tests
- Add data-testid attributes to settings and new chat buttons
- Add list reporter for CI to show failures in logs
- Add Playwright browser caching to speed up CI
- Add vitest coverage configuration
- Fix conditional test assertions to use test.skip() instead of silent pass
- Remove unused variables flagged by linter

.github/workflows/test.yml

@@ -43,9 +43,21 @@ jobs:
       - name: Install dependencies
         run: npm ci
 
+      - name: Cache Playwright browsers
+        uses: actions/cache@v4
+        id: playwright-cache
+        with:
+          path: ~/.cache/ms-playwright
+          key: playwright-${{ runner.os }}-${{ hashFiles('**/package-lock.json') }}
+
       - name: Install Playwright browsers
+        if: steps.playwright-cache.outputs.cache-hit != 'true'
         run: npx playwright install chromium --with-deps
 
+      - name: Install Playwright deps (cached)
+        if: steps.playwright-cache.outputs.cache-hit == 'true'
+        run: npx playwright install-deps chromium
+
       - name: Build app
         run: npm run build