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-lock.json

@@ -18,6 +18,7 @@
         "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",
@@ -660,6 +661,21 @@
         "pako": "^1.0.10"
       }
     },
+    "node_modules/@playwright/test": {
+      "version": "1.62.0",
+      "resolved": "https://registry.npmjs.org/@playwright/test/-/test-1.62.0.tgz",
+      "integrity": "sha512-9zOJ6ZQRAena31MpOH9VSzIz8Ou3YJ/wtY/eQm5T2uhfhG7/U3COrMS8xOtUrZrp9OgdmzEnIYODye3nY1VqzA==",
+      "dev": true,
+      "dependencies": {
+        "playwright": "1.62.0"
+      },
+      "bin": {
+        "playwright": "cli.js"
+      },
+      "engines": {
+        "node": ">=20"
+      }
+    },
     "node_modules/@rolldown/binding-android-arm64": {
       "version": "1.1.4",
       "resolved": "https://registry.npmjs.org/@rolldown/binding-android-arm64/-/binding-android-arm64-1.1.4.tgz",
@@ -2408,6 +2424,50 @@
         "url": "https://github.com/sponsors/jonschlinkert"
       }
     },
+    "node_modules/playwright": {
+      "version": "1.62.0",
+      "resolved": "https://registry.npmjs.org/playwright/-/playwright-1.62.0.tgz",
+      "integrity": "sha512-Z14dG305dgaLu6foB1TXQagFiW8JfSUIUaUuPaKQ6NtBPKF1P/qXcqfh6c6K/icPqdy37JmjbiBXf6JNg6Sylw==",
+      "dev": true,
+      "dependencies": {
+        "playwright-core": "1.62.0"
+      },
+      "bin": {
+        "playwright": "cli.js"
+      },
+      "engines": {
+        "node": ">=20"
+      },
+      "optionalDependencies": {
+        "fsevents": "2.3.2"
+      }
+    },
+    "node_modules/playwright-core": {
+      "version": "1.62.0",
+      "resolved": "https://registry.npmjs.org/playwright-core/-/playwright-core-1.62.0.tgz",
+      "integrity": "sha512-nsNRyq0r2zsG8AcRHWknc9QRA5XCueC7gWMrs+Gx2tlZn9hcl8zudfh00lhJPY1DE7NmZ6bDsT9g2yey8mXljA==",
+      "dev": true,
+      "bin": {
+        "playwright-core": "cli.js"
+      },
+      "engines": {
+        "node": ">=20"
+      }
+    },
+    "node_modules/playwright/node_modules/fsevents": {
+      "version": "2.3.2",
+      "resolved": "https://registry.npmjs.org/fsevents/-/fsevents-2.3.2.tgz",
+      "integrity": "sha512-xiqMQR4xAeHTuB9uWm+fFRcIOgKBMiOBP+eXiyT7jsgVCq1bkVygt00oASowB7EdtpOHaaPgKt812P9ab+DDKA==",
+      "dev": true,
+      "hasInstallScript": true,
+      "optional": true,
+      "os": [
+        "darwin"
+      ],
+      "engines": {
+        "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
+      }
+    },
     "node_modules/postcss": {
       "version": "8.5.16",
       "resolved": "https://registry.npmjs.org/postcss/-/postcss-8.5.16.tgz",