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/components/settings/DockerSettings.tsx

@@ -121,9 +121,9 @@ export default function DockerSettings() {
         )}
 
         {/* Resolved image display */}
-        <div className="flex items-center justify-between">
+        <div>
           <span className="text-[var(--text-secondary)]">Image</span>
-          <span className="text-xs text-[var(--text-secondary)] truncate max-w-[200px]" title={resolvedImageName}>
+          <span className="block text-xs text-[var(--text-secondary)] font-mono mt-0.5 truncate" title={resolvedImageName}>
             {resolvedImageName}
           </span>
         </div>