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/package.json

@@ -20,6 +20,7 @@
     "yjs": "^13.6.0"
   },
   "devDependencies": {
+    "@playwright/test": "^1.62.0",
     "@testing-library/dom": "^10.4.1",
     "@testing-library/jest-dom": "^6.9.1",
     "@testing-library/react": "^16.3.2",