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. - 

{
    auto lock1 = lockForShare(local_context->getCurrentQueryId(), local_context->getSettingsRef().lock_acquire_timeout);
    auto lock2 = dest_table->lockForShare(local_context->getCurrentQueryId(), local_context->getSettingsRef().lock_acquire_timeout);
    auto dest_table_storage = std::dynamic_pointer_cast<StorageMergeTree>(dest_table);
    if (!dest_table_storage)
        throw Exception("Table " + getStorageID().getNameForLogs() + " supports movePartitionToTable only for MergeTree family of table engines."
                        " Got " + dest_table->getName(), ErrorCodes::NOT_IMPLEMENTED);
    if (dest_table_storage->getStoragePolicy() != this->getStoragePolicy())
        throw Exception("Destination table " + dest_table_storage->getStorageID().getNameForLogs() +
                       " should have the same storage policy of source table " + getStorageID().getNameForLogs() + ". " +
                       getStorageID().getNameForLogs() + ": " + this->getStoragePolicy()->getName() + ", " +
                       dest_table_storage->getStorageID().getNameForLogs() + ": " + dest_table_storage->getStoragePolicy()->getName(), ErrorCodes::UNKNOWN_POLICY);
    auto dest_metadata_snapshot = dest_table->getInMemoryMetadataPtr();
    auto metadata_snapshot = getInMemoryMetadataPtr();
    Stopwatch watch;
    MergeTreeData & src_data = dest_table_storage->checkStructureAndGetMergeTreeData(*this, metadata_snapshot, dest_metadata_snapshot);
    String partition_id = getPartitionIDFromQuery(partition, local_context);
    DataPartsVector src_parts = src_data.getDataPartsVectorInPartition(MergeTreeDataPartState::Committed, partition_id);
    MutableDataPartsVector dst_parts;
    static const String TMP_PREFIX = "tmp_move_from_";
    for (const DataPartPtr & src_part : src_parts)
    {
        if (!dest_table_storage->canReplacePartition(src_part))
            throw Exception(
                "Cannot move partition '" + partition_id + "' because part '" + src_part->name + "' has inconsistent granularity with table",
                ErrorCodes::LOGICAL_ERROR);
        
        Int64 temp_index = insert_increment.get();
        MergeTreePartInfo dst_part_info(partition_id, temp_index, temp_index, src_part->info.level);