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-tauri/src/lib.rs

@@ -119,6 +119,7 @@ pub fn run() {
             // Updates
             commands::update_commands::get_app_version,
             commands::update_commands::check_for_updates,
+            commands::update_commands::check_image_update,
         ])
         .run(tauri::generate_context!())
         .expect("error while running tauri application");