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/hooks/useUpdates.ts

@@ -6,16 +6,25 @@ import * as commands from "../lib/tauri-commands";
 const CHECK_INTERVAL_MS = 24 * 60 * 60 * 1000; // 24 hours
 
 export function useUpdates() {
-  const { updateInfo, setUpdateInfo, appVersion, setAppVersion, appSettings } =
-    useAppState(
-      useShallow((s) => ({
-        updateInfo: s.updateInfo,
-        setUpdateInfo: s.setUpdateInfo,
-        appVersion: s.appVersion,
-        setAppVersion: s.setAppVersion,
-        appSettings: s.appSettings,
-      })),
-    );
+  const {
+    updateInfo,
+    setUpdateInfo,
+    imageUpdateInfo,
+    setImageUpdateInfo,
+    appVersion,
+    setAppVersion,
+    appSettings,
+  } = useAppState(
+    useShallow((s) => ({
+      updateInfo: s.updateInfo,
+      setUpdateInfo: s.setUpdateInfo,
+      imageUpdateInfo: s.imageUpdateInfo,
+      setImageUpdateInfo: s.setImageUpdateInfo,
+      appVersion: s.appVersion,
+      setAppVersion: s.setAppVersion,
+      appSettings: s.appSettings,
+    })),
+  );
 
   const intervalRef = useRef<ReturnType<typeof setInterval> | null>(null);
 
@@ -47,11 +56,31 @@ export function useUpdates() {
     }
   }, [setUpdateInfo, appSettings?.dismissed_update_version]);
 
+  const checkImageUpdate = useCallback(async () => {
+    try {
+      const info = await commands.checkImageUpdate();
+      if (info) {
+        // Respect dismissed image digest
+        const dismissed = appSettings?.dismissed_image_digest;
+        if (dismissed && dismissed === info.remote_digest) {
+          setImageUpdateInfo(null);
+          return null;
+        }
+      }
+      setImageUpdateInfo(info);
+      return info;
+    } catch (e) {
+      console.error("Failed to check for image updates:", e);
+      return null;
+    }
+  }, [setImageUpdateInfo, appSettings?.dismissed_image_digest]);
+
   const startPeriodicCheck = useCallback(() => {
     if (intervalRef.current) return;
     intervalRef.current = setInterval(() => {
       if (appSettings?.auto_check_updates !== false) {
         checkForUpdates();
+        checkImageUpdate();
       }
     }, CHECK_INTERVAL_MS);
     return () => {
@@ -60,13 +89,15 @@ export function useUpdates() {
         intervalRef.current = null;
       }
     };
-  }, [checkForUpdates, appSettings?.auto_check_updates]);
+  }, [checkForUpdates, checkImageUpdate, appSettings?.auto_check_updates]);
 
   return {
     updateInfo,
+    imageUpdateInfo,
     appVersion,
     loadVersion,
     checkForUpdates,
+    checkImageUpdate,
     startPeriodicCheck,
   };
 }