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. - 

{
    std::lock_guard moving_lock(moving_parts_mutex);
    MergeTreeMovingParts parts_to_move;
    for (const auto & part : parts)
    {
        auto reservation = space->reserve(part->getBytesOnDisk());
        if (!reservation)
            throw Exception("Move is not possible. Not enough space on '" + space->getName() + "'", ErrorCodes::NOT_ENOUGH_SPACE);
        auto reserved_disk = reservation->getDisk();
        if (reserved_disk->exists(relative_data_path + part->name))
            throw Exception(
                "Move is not possible: " + fullPath(reserved_disk, relative_data_path + part->name) + " already exists",
                ErrorCodes::DIRECTORY_ALREADY_EXISTS);
        if (currently_moving_parts.count(part) || partIsAssignedToBackgroundOperation(part))
            throw Exception(
                "Cannot move part '" + part->name + "' because it's participating in background process",
                ErrorCodes::PART_IS_TEMPORARILY_LOCKED);
        parts_to_move.emplace_back(part, std::move(reservation));
    }
    return std::make_shared<CurrentlyMovingPartsTagger>(std::move(parts_to_move), *this);
}
bool MergeTreeData::moveParts(const CurrentlyMovingPartsTaggerPtr & moving_tagger)