Adopt the new search backfill client interfaces.

ElementX/Sources/Services/Client/ClientProxy.swift

@@ -56,6 +56,8 @@ class ClientProxy: ClientProxyProtocol {
     
     private var delegateHandle: TaskHandle?
     
+    private var searchBackfillTaskHandle: TaskHandle?
+    
     // These following summary providers both operate on the same allRooms() list but
     // can apply their own filtering and pagination
     private(set) var roomSummaryProvider: RoomSummaryProviderProtocol
@@ -473,6 +475,25 @@ class ClientProxy: ClientProxyProtocol {
         await transitionServices(to: .suspended).value
     }
     
+    func startSearchBackfill(strategy: SearchBackfillStrategy) {
+        if strategy == .foreground, isSearchBackfillRunning {
+            return
+        }
+        
+        MXLog.info("Starting search backfill with strategy: \(strategy)")
+        searchBackfillTaskHandle?.cancel()
+        searchBackfillTaskHandle = client.runSearchBackfill(strategy: strategy)
+    }
+    
+    func stopSearchBackfill() {
+        searchBackfillTaskHandle?.cancel()
+        searchBackfillTaskHandle = nil
+    }
+    
+    var isSearchBackfillRunning: Bool {
+        searchBackfillTaskHandle?.isFinished() == false
+    }
+    
     func expireSyncSessions() async {
         await syncService.expireSessions()
     }
@@ -1188,6 +1209,8 @@ class ClientProxy: ClientProxyProtocol {
         case .suspended:
             updateHomeserverReachability()
             
+            stopSearchBackfill()
+            
             MXLog.info("Stopping sync")
             await syncService.stop()
             MXLog.info("Sync stopped")