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

.gitignore

@@ -11,3 +11,8 @@ dist/
 .DS_Store
 coverage/
 .vitest/
+
+# Playwright
+frontend/test-results/
+frontend/playwright-tests/screenshots/
+frontend/playwright-tests/*.json