Add WebDAV sync provider (manual + auto-sync, top-bar button)

src-tauri/src/state.rs

@@ -10,6 +10,7 @@ pub struct AppState {
     pub search_index: Mutex<Option<Arc<SearchIndex>>>,
     pub watcher: Mutex<Option<RecommendedWatcher>>,
     pub importing: AtomicBool,
+    pub syncing: AtomicBool,
     pub pending_open_file: Mutex<Option<String>>,
 }
 
@@ -20,6 +21,7 @@ impl AppState {
             search_index: Mutex::new(None),
             watcher: Mutex::new(None),
             importing: AtomicBool::new(false),
+            syncing: AtomicBool::new(false),
             pending_open_file: Mutex::new(None),
         }
     }