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/App.tsx

@@ -17,7 +17,7 @@ export default function App() {
   const { loadSettings } = useSettings();
   const { refresh } = useProjects();
   const { refresh: refreshMcp } = useMcpServers();
-  const { loadVersion, checkForUpdates, startPeriodicCheck } = useUpdates();
+  const { loadVersion, checkForUpdates, checkImageUpdate, startPeriodicCheck } = useUpdates();
   const { sessions, activeSessionId, setProjects } = useAppState(
     useShallow(s => ({ sessions: s.sessions, activeSessionId: s.activeSessionId, setProjects: s.setProjects }))
   );
@@ -46,7 +46,10 @@ export default function App() {
 
     // Update detection
     loadVersion();
-    const updateTimer = setTimeout(() => checkForUpdates(), 3000);
+    const updateTimer = setTimeout(() => {
+      checkForUpdates();
+      checkImageUpdate();
+    }, 3000);
     const cleanup = startPeriodicCheck();
     return () => {
       clearTimeout(updateTimer);