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 lock(existing_nodes_cache_mutex);
        if (existing_nodes_cache.count(path))
            return true;
    }
    bool res = getZooKeeper()->exists(path);
    if (res)
    {
        std::lock_guard lock(existing_nodes_cache_mutex);
        existing_nodes_cache.insert(path);
    }
    return res;
}
std::optional<EphemeralLockInZooKeeper>