fix(frontend): resolve TypeScript errors in simple mode implementation

- Remove unused simpleMode variable in AppSidebar.vue
- Add run_mode to AuthResponse.user type definition

frontend/src/components/layout/AppSidebar.vue

@@ -154,7 +154,6 @@ const isDark = ref(document.documentElement.classList.contains('dark'))
 const siteName = computed(() => appStore.siteName)
 const siteLogo = computed(() => appStore.siteLogo)
 const siteVersion = computed(() => appStore.siteVersion)
-const simpleMode = computed(() => appStore.simpleMode)
 
 // SVG Icon Components
 const DashboardIcon = {

frontend/src/types/index.ts

@@ -61,7 +61,7 @@ export interface PublicSettings {
 export interface AuthResponse {
   access_token: string
   token_type: string
-  user: User
+  user: User & { run_mode?: 'standard' | 'simple' }
 }
 
 export interface CurrentUserResponse extends User {