I finally managed to solve the problem in Python. It's not perfect but it works:

Class User.Timer Extends %RegisteredObject
{

Property Executor [ Private ];

Method Initialize(maxWorkers As %Integer = 4) [ Language = python ]
{
import concurrent.futures
import time
import threading

self.Executor = concurrent.futures.ThreadPoolExecutor(max_workers=maxWorkers)
}

Method Close() [ Language = python ]
{
if self.Executor:
	self.Executor.shutdown()
}

Method Greet(name)
{
	Write "Hello ", name, !
}

Method OnCallback0(methodName As %String) [ Private ]
{
	Do $METHOD(instance, methodName)
}

Method OnCallback1(instance As %RegisteredObject, method As %String, arg1) [ Private ]
{
	Do $METHOD(instance, method, arg1)
}

Method OnCallback2(instance As %RegisteredObject, method As %String, arg1, arg2) [ Private ]
{
	Do $METHOD(instance, method, arg1, arg2)
}

Method OnCallback3(instance As %RegisteredObject, method As %String, arg1, arg2, arg3) [ Private ]
{
	Do $METHOD(instance, method, arg1, arg2, arg3)
}

Method OnCallback4(instance As %RegisteredObject, method As %String, arg1, arg2, arg3, arg4) [ Private ]
{
	Do $METHOD(instance, method, arg1, arg2, arg3, arg4)
}

Method OnCallback5(instance As %RegisteredObject, method As %String, arg1, arg2, arg3, arg4, arg5) [ Private ]
{
	Do $METHOD(instance, method, arg1, arg2, arg3, arg4, arg5)
}

Method InternalRun(delayMs As %Integer, wait As %Boolean, instance As %RegisteredObject, method As %String, args... As %List) [ Internal, Language = python ]
{
import time
import iris

if not self.Executor:
	raise Exception("The 'Initialize' method has not been called.")

def worker_function():
    time.sleep(delayMs / 1000)
    if len(args) == 0:
    	self.OnCallback0(instance, method)
    elif len(args) == 1:
        self.OnCallback1(instance, method, args[0])
    elif len(args) == 2:
        self.OnCallback2(instance, method, args[0], args[1])
    elif len(args) == 3:
        self.OnCallback3(instance, method, args[0], args[1], args[2])
    elif len(args) == 4:
        self.OnCallback4(instance, method, args[0], args[1], args[2], args[3])
    elif len(args) == 5:
        self.OnCallback5(instance, method, args[0], args[1], args[2], args[3], args[4])
    else:
        raise Exception("Too many arguments.")
    return 0
    
        
future = self.Executor.submit(worker_function)

# wait == 0 means fire-and-forget
try:
    if (wait == 1):
        rv = future.result()
    
except Exception as e:
    print(f"{e}")
}

/// delayMs  - the parameter specifies the timer delay in milliseconds
/// wait     - if the parameter is false, the process will not wait for the Future result to be returned (fire-and-forget)
/// instance - any object which method should be called with a delay
/// method   - specifies the object's callback method name
/// args     - the callback method arguments (up to 5)
Method Run(delayMs As %Integer, wait As %Boolean, instance As %RegisteredObject, method As %String, args... As %List)
{
	Do ..InternalRun(delayMs, wait, instance, method, args...)
}

ClassMethod Test()
{
	Set obj = ##class(Timer).%New()
	Do obj.Initialize()
	Do obj.Run(1000, 0, obj, "Greet", "John")
	Do obj.Run(2000, 0, obj, "Greet", "Jessica")
	Write "If 'wait == 0' this line will be printed first", !
	Do obj.Close()
}

}

Here it is (implemented as Mixin):

Class MyNamespace.Pooled Extends Ens.Host [ Abstract ]
{

Property PoolIndex As %Integer [ Calculated ];

Method PoolIndexGet() As %Integer
{
    #Dim cn as %String
    Set cn = ..%ConfigName	
	
    #Dim statement as %SQL.Statement
    Set statement = ##class(%SQL.Statement).%New()
    Set status = statement.%PrepareClassQuery("Ens.Job","Enumerate")
    $$$ThrowOnError(status)
    
    #Dim rs as %SQL.StatementResult
    Set rs = statement.%Execute()
    #Dim i as %Integer = -1
    
    While (rs.%Next()) 
    {
		#Dim jobId as %String 
		Set jobId = rs.%Get("Job")
		If (rs.%Get("ConfigName") = cn)
		{
			Set i = i + 1
			If (jobId = $JOB) 
			{
				Kill rs
				Return i
			}
		}
    }
    Kill rs
    Return i
}

Property PoolSize As %Integer [Calculated];

Method PoolSizeGet() As %Integer
{
    #Dim cn as %String
    Set cn = ..%ConfigName
    #Dim statement as %SQL.Statement
    Set statement = ##class(%SQL.Statement).%New()
    Set status = statement.%PrepareClassQuery("Ens.Job","Enumerate")
    $$$ThrowOnError(status)
   
    #Dim rs as %SQL.StatementResult
    Set rs = statement.%Execute()
    #Dim i as %Integer = 0
    
    While (rs.%Next()) 
    {
		If (rs.%Get("ConfigName") = cn)
		{
			Set i = i + 1
		}
    }
    Kill rs
    Return i
}

}

Found the answer. It is simply not allowed: "+ Rule: For collections of type document, message, searchset or collection, all entries must contain resources, and not have request or response elements"

The error has gone after IRIS restart. Another indicator of the problem was that the SQL Gateway connection test was not working