feat: replace screen state machine with React Router v7 URL routing

- Install react-router-dom
- Add slugify utility with full TDD test suite (7 tests)
- Wrap app in BrowserRouter in main.tsx
- Add optional onNavigate prop to ExamRunner.goTo
- Create ExamRoute component (deep-link restore + back/forward sync)
- Migrate App.tsx: replace screen useState with <Routes>, all setScreen()
  calls replaced with navigate(), add activateExam for deep-link activation,
  use useLocation for verify/reset-password special layouts
- Remove unused AppScreen type from types.ts

frontend/package-lock.json

@@ -11,7 +11,8 @@
         "dompurify": "^3.4.1",
         "katex": "^0.16.45",
         "react": "^19.2.5",
-        "react-dom": "^19.2.5"
+        "react-dom": "^19.2.5",
+        "react-router-dom": "^7.14.2"
       },
       "devDependencies": {
         "@babel/core": "^7.29.0",
@@ -1791,6 +1792,19 @@
       "dev": true,
       "license": "MIT"
     },
+    "node_modules/cookie": {
+      "version": "1.1.1",
+      "resolved": "https://registry.npmjs.org/cookie/-/cookie-1.1.1.tgz",
+      "integrity": "sha512-ei8Aos7ja0weRpFzJnEA9UHJ/7XQmqglbRwnf2ATjcB9Wq874VKH9kfjjirM6UhU2/E5fFYadylyhFldcqSidQ==",
+      "license": "MIT",
+      "engines": {
+        "node": ">=18"
+      },
+      "funding": {
+        "type": "opencollective",
+        "url": "https://opencollective.com/express"
+      }
+    },
     "node_modules/cross-spawn": {
       "version": "7.0.6",
       "resolved": "https://registry.npmjs.org/cross-spawn/-/cross-spawn-7.0.6.tgz",
@@ -3075,6 +3089,44 @@
         "react": "^19.2.5"
       }
     },
+    "node_modules/react-router": {
+      "version": "7.14.2",
+      "resolved": "https://registry.npmjs.org/react-router/-/react-router-7.14.2.tgz",
+      "integrity": "sha512-yCqNne6I8IB6rVCH7XUvlBK7/QKyqypBFGv+8dj4QBFJiiRX+FG7/nkdAvGElyvVZ/HQP5N19wzteuTARXi5Gw==",
+      "license": "MIT",
+      "dependencies": {
+        "cookie": "^1.0.1",
+        "set-cookie-parser": "^2.6.0"
+      },
+      "engines": {
+        "node": ">=20.0.0"
+      },
+      "peerDependencies": {
+        "react": ">=18",
+        "react-dom": ">=18"
+      },
+      "peerDependenciesMeta": {
+        "react-dom": {
+          "optional": true
+        }
+      }
+    },
+    "node_modules/react-router-dom": {
+      "version": "7.14.2",
+      "resolved": "https://registry.npmjs.org/react-router-dom/-/react-router-dom-7.14.2.tgz",
+      "integrity": "sha512-YZcM5ES8jJSM+KrJ9BdvHHqlnGTg5tH3sC5ChFRj4inosKctdyzBDhOyyHdGk597q2OT6NTrCA1OvB/YDwfekQ==",
+      "license": "MIT",
+      "dependencies": {
+        "react-router": "7.14.2"
+      },
+      "engines": {
+        "node": ">=20.0.0"
+      },
+      "peerDependencies": {
+        "react": ">=18",
+        "react-dom": ">=18"
+      }
+    },
     "node_modules/resolve-from": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/resolve-from/-/resolve-from-4.0.0.tgz",
@@ -3142,6 +3194,12 @@
         "semver": "bin/semver.js"
       }
     },
+    "node_modules/set-cookie-parser": {
+      "version": "2.7.2",
+      "resolved": "https://registry.npmjs.org/set-cookie-parser/-/set-cookie-parser-2.7.2.tgz",
+      "integrity": "sha512-oeM1lpU/UvhTxw+g3cIfxXHyJRc/uidd3yK1P242gzHds0udQBYzs3y8j4gCCW+ZJ7ad0yctld8RYO+bdurlvw==",
+      "license": "MIT"
+    },
     "node_modules/shebang-command": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/shebang-command/-/shebang-command-2.0.0.tgz",