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. - 

if (it_part == data_parts_by_info.end())
        throw Exception("No such data part " + part_to_detach->getNameWithState(), ErrorCodes::NO_SUCH_DATA_PART);
    
    DataPartPtr part = *it_part;
    if (part->getState() == DataPartState::Committed)
    {
        removePartContributionToDataVolume(part);
        removePartContributionToColumnSizes(part);
    }
    modifyPartState(it_part, DataPartState::Deleting);
    part->renameToDetached(prefix);
    data_parts_indexes.erase(it_part);
    if (restore_covered && part->info.level == 0)
    {
        LOG_WARNING(log, "Will not recover parts covered by zero-level part {}", part->name);
        return;
    }
    if (restore_covered)
    {
        Strings restored;
        bool error = false;
        String error_parts;
        Int64 pos = part->info.min_block;
        auto is_appropriate_state = [] (DataPartState state)
        {
            return state == DataPartState::Committed || state == DataPartState::Outdated;
        };
        auto update_error = [&] (DataPartIteratorByInfo it)
        {
            error = true;