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

components/chat-panel.tsx

@@ -1185,6 +1185,7 @@ export default function ChatPanel({
                                 status === "streaming" || status === "submitted"
                             }
                             className="hover:bg-accent disabled:opacity-50 disabled:cursor-not-allowed"
+                            data-testid="new-chat-button"
                         >
                             <MessageSquarePlus
                                 className={`${isMobile ? "h-4 w-4" : "h-5 w-5"} text-muted-foreground`}
@@ -1197,6 +1198,7 @@ export default function ChatPanel({
                             size="icon"
                             onClick={() => setShowSettingsDialog(true)}
                             className="hover:bg-accent"
+                            data-testid="settings-button"
                         >
                             <Settings
                                 className={`${isMobile ? "h-4 w-4" : "h-5 w-5"} text-muted-foreground`}