feat(auth): [PM-13659] implement 2FA timeout handling across clients

Add timeout state management for two-factor authentication flows in web, desktop,
and browser extension clients. Includes:

- New timeout screen component with 5-minute session limit
- Updated UI elements and styling
- Comprehensive test coverage

Refs: PM-13659

apps/browser/src/_locales/en/messages.json

@@ -1319,6 +1319,12 @@
   "enterVerificationCodeApp": {
     "message": "Enter the 6 digit verification code from your authenticator app."
   },
+  "authenticationTimeout": {
+    "message": "Authentication timeout"
+  },
+  "authenticationSessionTimedOut": {
+    "message": "The authentication session timed out. Please restart the login process."
+  },
   "enterVerificationCodeEmail": {
     "message": "Enter the 6 digit verification code that was emailed to $EMAIL$.",
     "placeholders": {

apps/browser/src/popup/app-routing.module.ts

@@ -6,6 +6,7 @@ import {
   EnvironmentSelectorRouteData,
   ExtensionDefaultOverlayPosition,
 } from "@bitwarden/angular/auth/components/environment-selector.component";
+import { TwoFactorTimeoutComponent } from "@bitwarden/angular/auth/components/two-factor-auth/two-factor-auth-expired.component";
 import { unauthUiRefreshRedirect } from "@bitwarden/angular/auth/functions/unauth-ui-refresh-redirect";
 import { unauthUiRefreshSwap } from "@bitwarden/angular/auth/functions/unauth-ui-refresh-route-swap";
 import {
@@ -38,6 +39,7 @@ import {
   VaultIcon,
   LoginDecryptionOptionsComponent,
   DevicesIcon,
+  TwoFactorTimeoutIcon,
 } from "@bitwarden/auth/angular";
 import { FeatureFlag } from "@bitwarden/common/enums/feature-flag.enum";
 
@@ -199,6 +201,29 @@ const routes: Routes = [
       ],
     },
   ),
+  {
+    path: "",
+    component: ExtensionAnonLayoutWrapperComponent,
+    children: [
+      {
+        path: "2fa-timeout",
+        canActivate: [unauthGuardFn(unauthRouteOverrides)],
+        children: [
+          {
+            path: "",
+            component: TwoFactorTimeoutComponent,
+          },
+        ],
+        data: {
+          pageTitle: {
+            key: "authenticationTimeout",
+          },
+          pageIcon: TwoFactorTimeoutIcon,
+          elevation: 1,
+        } satisfies RouteDataProperties & AnonLayoutWrapperData,
+      },
+    ],
+  },
   {
     path: "2fa-options",
     component: TwoFactorOptionsComponent,