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

vitest.config.mts

@@ -7,5 +7,11 @@ export default defineConfig({
     test: {
         environment: "jsdom",
         include: ["tests/**/*.test.{ts,tsx}"],
+        coverage: {
+            provider: "v8",
+            reporter: ["text", "json", "html"],
+            include: ["lib/**/*.ts", "app/**/*.ts", "app/**/*.tsx"],
+            exclude: ["**/*.test.ts", "**/*.test.tsx", "**/*.d.ts"],
+        },
     },
 })