Azure Service Bus Queue: re-schedule messages while increasing deliveryCount

I use Azure Service Bus Queues to collect messages that need to be posted to an API. I’m using an Azure trigger function on the Queue to process incoming messages.
Unfortunately, the API is unreliable so I’m working on adding my own retry schedule.

For example, the first time a message couldn’t be processed, I want to schedule another retry in 15 minutes, and after that 1h, 2h and so on. Once the maxDeliveryCount has been reached, messages should be sent to the DLQ.

The scheduling of the messages is working, however, each scheduled message is seen as a new message, meaning that the deliveryCount is always 1. I’m using the @azure/service-bus NPM package to do the rescheduling in the Azure function.

Therefore, my question is:
How can I reschedule SB Queue messages in an Azure trigger function while increasing the deliveryCount of those messages?

(I’m aware that I could add my own deliveryCount property to the message, but I’d rather not pollute the message body with metadata.)

To provide some more details, this is a MRE:

const serviceBusQueueTrigger: AzureFunction = async function (
  context: Context,
  msg: any
): Promise<void> {
  context.log("ServiceBus queue trigger function processed message", msg);


  const serviceBusClient = new ServiceBusClient(<connection_string>);
  const sender = serviceBusClient.createSender(<queue_name>);

  context.log("dequeueCount: ", context.bindingData.deliveryCount);

  try {
    // POST to API
  } catch (error) {
    
    // if an error is thrown here, trigger resubmits immediately
    // I want to wait proportionally to current deliveryCount
    
    await sender.scheduleMessages(
      {
        body: msgData,
        contentType: "application/json",
      },
      // just an example of schedule time
      new Date(Date.now() + Math.pow(2, context.bindingData.deliveryCount) * 60 * 1000)
    );
  }
  
  await sender.close();
}

===

Edit: Although the Microsoft Docs still contain (vague) details about the built-in retry mechanism (which @Manish linked in his answer), the functionality seems no longer supported. The relevant discussion can be found here.

Therefore, my initial question stands, how can I build this mechanism using an Azure Service Bus Trigger Function? Thanks!

host.json

{
  "version": "2.0",
  "logging": {
    "applicationInsights": {
      "samplingSettings": {
        "isEnabled": true,
        "excludedTypes": "Request"
      }
    }
  },
  "extensionBundle": {
    "id": "Microsoft.Azure.Functions.ExtensionBundle",
    "version": "[4.0.0, 5.0.0)"
  },
  "concurrency": {
    "dynamicConcurrencyEnabled": true,
    "snapshotPersistenceEnabled": true
  },
  "extensions": {
    "serviceBus": {
      "clientRetryOptions": {
        "mode": "exponential",
        "tryTimeout": "00:01:00",
        "delay": "00:01:00",
        "maxDelay": "03:00:00",
        "maxRetries": 3
      }
    }
  }
}

function.json

{
  "bindings": [
    {
      "name": "incoming",
      "type": "serviceBusTrigger",
      "direction": "in",
      "queueName": "incoming",
      "connection": "SERVICEBUS"
    }
  ],
  "retry": {
    "strategy": "exponentialBackoff",
    "maxRetryCount": 5,
    "minimumInterval": "00:00:10",
    "maximumInterval": "00:15:00"
  },
  "scriptFile": "../dist/trigger/index.js"
}