fix: get_connectivity(): Get rid of locking SchedulerState::inner (#7124)

`get_connectivity()` is expected to return immediately, not when the scheduler finishes updating its
state in `start_io()/stop_io()/pause_io()`, otherwise it causes app non-responsiveness.

Instead of read-locking `SchedulerState::inner`, store the `ConnectivityStore` collection in
`Context` and fetch it from there in `get_connectivity()`. Update it every time we release a write
lock on `SchedulerState::inner`.

src/imex/transfer.rs

@@ -105,7 +105,7 @@ impl BackupProvider {
 
         // Acquire global "ongoing" mutex.
         let cancel_token = context.alloc_ongoing().await?;
-        let paused_guard = context.scheduler.pause(context.clone()).await?;
+        let paused_guard = context.scheduler.pause(context).await?;
         let context_dir = context
             .get_blobdir()
             .parent()