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. - 

{
    String partition_id;
    if (moving_part)
        partition_id = partition->as<ASTLiteral &>().value.safeGet<String>();
    else
        partition_id = getPartitionIDFromQuery(partition, local_context);
    DataPartsVector parts;
    if (moving_part)
    {
        auto part_info = MergeTreePartInfo::fromPartName(partition_id, format_version);
        parts.emplace_back(getActiveContainingPart(part_info));
        if (!parts.back() || parts.back()->name != part_info.getPartName())
            throw Exception("Part " + partition_id + " is not exists or not active", ErrorCodes::NO_SUCH_DATA_PART);
    }
    else
        parts = getDataPartsVectorInPartition(MergeTreeDataPartState::Committed, partition_id);
    auto volume = getStoragePolicy()->getVolumeByName(name);
    if (!volume)
        throw Exception("Volume " + name + " does not exists on policy " + getStoragePolicy()->getName(), ErrorCodes::UNKNOWN_DISK);
    if (parts.empty())
        throw Exception("Nothing to move (сheck that the partition exists).", ErrorCodes::NO_SUCH_DATA_PART);
    parts.erase(std::remove_if(parts.begin(), parts.end(), [&](auto part_ptr)
        {
            for (const auto & disk : volume->getDisks())
            {
                if (part_ptr->volume->getDisk()->getName() == disk->getName())
                {
                    return true;