Rename AuthMode to Backend, fix LiteLLM variant typo, add image update alerts, clean up Settings

- Fix serde deserialization error: TypeScript sent "lit_llm" but Rust expected "lite_llm"
- Rename AuthMode enum to Backend across Rust and TypeScript (with serde alias for backward compat)
- Add container image update checking via registry digest comparison
- Improve Settings page: fix image address display spacing, remove per-project auth section
- Update UI labels from "Auth" to "Backend" throughout

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

app/src/lib/tauri-commands.ts

@@ -1,5 +1,5 @@
 import { invoke } from "@tauri-apps/api/core";
-import type { Project, ProjectPath, ContainerInfo, SiblingContainer, AppSettings, UpdateInfo, McpServer, FileEntry } from "./types";
+import type { Project, ProjectPath, ContainerInfo, SiblingContainer, AppSettings, UpdateInfo, ImageUpdateInfo, McpServer, FileEntry } from "./types";
 
 // Docker
 export const checkDocker = () => invoke<boolean>("check_docker");
@@ -83,3 +83,5 @@ export const uploadFileToContainer = (projectId: string, hostPath: string, conta
 export const getAppVersion = () => invoke<string>("get_app_version");
 export const checkForUpdates = () =>
   invoke<UpdateInfo | null>("check_for_updates");
+export const checkImageUpdate = () =>
+  invoke<ImageUpdateInfo | null>("check_image_update");