I have reproduced in my environment and got expected results and I followed the below process:
In my run.csx:
using System;
using System.Threading.Tasks;
public static void Run(string myQueueItem, ILogger log,ICollector<string> outputQueueItem)
{
log.LogInformation($"C# ServiceBus queue trigger function processed message: {myQueueItem}");
outputQueueItem.Add(myQueueItem);
}

In my Integration i added output as below:

In function.json:
{
"bindings": [
{
"name": "myQueueItem",
"connection": "Con",
"queueName": "rithwik",
"direction": "in",
"type": "serviceBusTrigger"
},
{
"name": "outputQueueItem",
"direction": "out",
"type": "queue",
"connection": "AzureWebJobsStorage",
"queueName": "outqueue"
}
]
}
Sent message in Service bus queue as below:

In my stoarge account a new queue is created as below and I got the message too:


So you need to add ouputQueueItem.Add inside the code and ICollector<string> outputQueueItem in parameters as my example. Now you will get output also as I have got.
Edit:
I have added few lines in my code please check:
run.csx:
using System;
using System.Threading.Tasks;
public static void Run(string myQueueItem, ILogger log,ICollector<string> outputQueueItem,TextWriter outputBlob)
{
log.LogInformation($"C# ServiceBus queue trigger function processed message: {myQueueItem}");
outputQueueItem.Add(myQueueItem);
outputBlob.WriteLine(myQueueItem);
}
function.json:
{
"bindings": [
{
"name": "myQueueItem",
"connection": "Con",
"queueName": "rithwik",
"direction": "in",
"type": "serviceBusTrigger"
},
{
"name": "outputQueueItem",
"direction": "out",
"type": "queue",
"connection": "AzureWebJobsStorage",
"queueName": "outqueue"
},
{
"name": "outputBlob",
"direction": "out",
"type": "blob",
"path": "outcontainer/{rand-guid}",
"connection": "AzureWebJobsStorage"
}
]
}
In integration:

Container and blob got created as below:

Inside container:

So, I am making few changes such as TextWriter as parameter and WriteLine inside code we can get expected results, hope this clears your doubt.
bodyof the request. I am new to Azure and my assumption was using output binding will do the needful (adding required output binding and attributes)