feat: enhance UI, fix backend routes, and add E2E quality gates

- UI: Polish PlanView toggles, buttons, and fix missing icons (running/activity).
- Backend: Fix route shadowing in main.py, add startup route check, and improve API test coverage.
- Tests: Add Playwright E2E smoke test, eslint-plugin-import, and integrate all into 'make check'.

.gitignore

@@ -38,3 +38,7 @@ backend/.garth/
 .vscode/
 .idea/
 .DS_Store
+
+# Playwright
+frontend/test-results/
+frontend/playwright-report/