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/models/update_info.rs

@@ -35,3 +35,14 @@ pub struct GiteaAsset {
     pub browser_download_url: String,
     pub size: u64,
 }
+
+/// Info returned to the frontend about an available container image update.
+#[derive(Debug, Clone, Serialize, Deserialize)]
+pub struct ImageUpdateInfo {
+    /// The remote digest (e.g. sha256:abc...)
+    pub remote_digest: String,
+    /// The local digest, if available
+    pub local_digest: Option<String>,
+    /// When the remote image was last updated (if known)
+    pub remote_updated_at: Option<String>,
+}