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. - 

renamed_parts.addPart(part_id, "attaching_" + part_id);
        if (MergeTreePartInfo::tryParsePartName(part_id, nullptr, format_version))
            name_to_disk[part_id] = getDiskForPart(part_id, source_dir);
    }
    else
    {
        String partition_id = getPartitionIDFromQuery(partition, local_context);
        LOG_DEBUG(log, "Looking for parts for partition {} in {}", partition_id, source_dir);
        ActiveDataPartSet active_parts(format_version);
        const auto disks = getStoragePolicy()->getDisks();
        for (const auto & disk : disks)
        {
            for (auto it = disk->iterateDirectory(relative_data_path + source_dir); it->isValid(); it->next())
            {
                const String & name = it->name();
                MergeTreePartInfo part_info;
                /
                /
                if (!MergeTreePartInfo::tryParsePartName(name, &part_info, format_version)
                    || part_info.partition_id != partition_id)
                {
                    continue;
                }
                LOG_DEBUG(log, "Found part {}", name);
                active_parts.add(name);
                name_to_disk[name] = disk;
            }
        }
        LOG_DEBUG(log, "{} of them are active", active_parts.size());
        /