Symptoms: all threads in BackgroundScheduledPool busy, lot of tasks in replication queue, none of the tasks is executing. 

![Screenshot from 2021-04-16 16-21-44_](https://user-images.githubusercontent.com/1549571/115193796-e767d600-a0ec-11eb-887c-5c9c2412e50c.png)

Related to #16895

Possible workarounds (poor options): increasing the background_schedule_pool_size to huge values, or restart server every time when that happens etc. - 

{
    Stopwatch watch;
    
    queue.pullLogsToQueue(getZooKeeper());
    
    
    background_executor.triggerTask();
    Poco::Event target_size_event;
    auto callback = [&target_size_event, queue_size] (size_t new_queue_size)
    {
        if (new_queue_size <= queue_size)
            target_size_event.set();
    };
    const auto handler = queue.addSubscriber(std::move(callback));
    while (!target_size_event.tryWait(50))
    {
        if (max_wait_milliseconds && watch.elapsedMilliseconds() > max_wait_milliseconds)
            return false;
        if (partial_shutdown_called)
            throw Exception("Shutdown is called for table", ErrorCodes::ABORTED);
    }
    return true;
}
bool StorageReplicatedMergeTree::dropPart(