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. - 

#include "StorageMergeTree.h"
#include <Databases/IDatabase.h>
#include <Common/escapeForFileName.h>
#include <Common/typeid_cast.h>
#include <Common/ThreadPool.h>
#include <Interpreters/InterpreterAlterQuery.h>
#include <Interpreters/PartLog.h>
#include <Interpreters/MutationsInterpreter.h>
#include <Interpreters/Context.h>
#include <Parsers/ASTCheckQuery.h>
#include <Parsers/ASTFunction.h>
#include <Parsers/ASTLiteral.h>
#include <Parsers/ASTPartition.h>
#include <Parsers/ASTSetQuery.h>
#include <Parsers/queryToString.h>
#include <Storages/MergeTree/MergeTreeData.h>
#include <Storages/MergeTree/ActiveDataPartSet.h>
#include <Storages/AlterCommands.h>
#include <Storages/PartitionCommands.h>
#include <Storages/MergeTree/MergeTreeBlockOutputStream.h>
#include <Storages/MergeTree/MergeTreeDataPartInMemory.h>
#include <Storages/MergeTree/PartitionPruner.h>
#include <Storages/MergeTree/MergeList.h>
#include <Storages/MergeTree/checkDataPart.h>
#include <Processors/Pipe.h>
#include <Processors/QueryPlan/BuildQueryPipelineSettings.h>
#include <Processors/QueryPlan/Optimizations/QueryPlanOptimizationSettings.h>
#include <optional>