fix: browser testing issues and missing UI tools

- Fix WebSocket URL to use ws:// for http development environments
- Make createLayer idempotent to prevent race-condition 500 under React StrictMode
- Add URL-based routing for /register so register page actually shows register form
- Add missing tool buttons to LeftSidebar: polygon, chair, extend, fillet
- Add Playwright browser test suite for exhaustive UI testing
- Update .gitignore for Playwright artifacts

Unit tests: backend 254/254, frontend 380/380

frontend/src/App.tsx

@@ -1778,7 +1778,10 @@ const CADEditor: React.FC<CADEditorProps> = ({ projectId, token, onNavigateBack
 // ─── App Wrapper (Auth Gate) ───────────────────────────
 const App: React.FC = () => {
   const { user, token } = useAuth();
-  const [authView, setAuthView] = useState<'login' | 'register'>('login');
+  const [authView, setAuthView] = useState<'login' | 'register'>(() => {
+    // URL-based routing: /register shows register form, otherwise login
+    return window.location.pathname === '/register' ? 'register' : 'login';
+  });
   const [openedProjectId, setOpenedProjectId] = useState<string | null>(null);
 
   // Not authenticated → show Login or Register