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. - 

const ASTPtr & partition, bool move_part, const String & to, ContextPtr )
{
    
    if (!move_part)
        throw Exception("MOVE PARTITION TO SHARD is not supported, use MOVE PART instead", ErrorCodes::NOT_IMPLEMENTED);
    if (normalizeZooKeeperPath(zookeeper_path) == normalizeZooKeeperPath(to))
        throw Exception("Source and destination are the same", ErrorCodes::BAD_ARGUMENTS);
    auto zookeeper = getZooKeeper();
    String part_name = partition->as<ASTLiteral &>().value.safeGet<String>();
    auto part_info = MergeTreePartInfo::fromPartName(part_name, format_version);
    auto part = getPartIfExists(part_info, {MergeTreeDataPartState::Committed});