.NET Azure Function Kafka Propagator

I am using latest .NET 9 for Azure Function and want to use distributed tracing accorss different Kafka messages that are created by Azure Functions and are read by other Azure Functions.

So far I am able to create tracing via

services.AddOpenTelemetry()
  .ConfigureResource(r => r.AddService("MyApplicationName", serviceVersion: "1.0"))
  .WithTracing(tracing =>
  {
      tracing.SetSampler(new AlwaysOnSampler());
      tracing.AddSource("MyApplicationName");
      tracing.AddAspNetCoreInstrumentation(o => { o.RecordException = true; });
      tracing.AddHttpClientInstrumentation(o => { o.RecordException = true; });
      tracing.AddEntityFrameworkCoreInstrumentation();
      tracing.AddNpgsql();

      tracing.AddOtlpExporter(name: "OtlpTracing", configure: null);
  });

services.AddSingleton(TracerProvider.Default.GetTracer(tracerSourceName));

The traces are written to Seq. This works so far.

In order to create a new trace I create a new RootActivity via Helper class

public static class Tracing
{
    public static readonly ActivitySource Source = new(
        Constants.ApplicationName.ToTraceName(),
        Constants.ApplicationVersion);

    public static RootActivity StartRootActivity(this ActivitySource source,
        string name,
        ActivityKind kind = ActivityKind.Internal,
        IEnumerable<KeyValuePair<string, object?>>? tags = null)
    {
        var parent = Activity.Current;
        Activity.Current = null;
        var next = source.StartActivity(name, kind,
            parentContext: default,
            tags: tags,
            links: new[] { new ActivityLink(parent.Context) });

        return new RootActivity(next, parent);
    }
}

public class RootActivity : IDisposable
{
    public Activity Activity { get; }
    public Activity ParentActivity { get; }

    public RootActivity(Activity activity, Activity parentActivity)
    {
        Activity = activity;
        ParentActivity = parentActivity;
    }

    private bool disposedValue;
    protected virtual void Dispose(bool disposing)
    {
        if (!disposedValue)
        {
            if (disposing)
            {
                Activity?.Dispose();
                Activity.Current = ParentActivity;
            }

            disposedValue = true;
        }
    }

    public void Dispose()
    {
        Dispose(disposing: true);
        GC.SuppressFinalize(this);
    }
}

In my function I then create a trace via

using var parentTrace = Tracing.Source.StartRootActivity("Linked Trace");

and the output of the function is written to a Kafka Queue following Microsoft Azure Function Kafka documentation (link).

[KafkaOutput("%KafkaBrokerList%",
             "%KafkaTopic_UploadDocument%",
             Username = "%KafkaUsername%",
             Password = "%KafkaPassword%",
             AuthenticationMode = BrokerAuthenticationMode.Plain)]
public UploadDocumentModel[]? KafkaEventUploadDocument { get; set; }

I have trouble adding a Propagator for distributed tracing. When reading a Kafka message, I would like my trace to be continued accross different Azure Functions.

I have read, that for distributed tracing a propagator is used, but I don't know how to implement it in Azure Functions as all examples are for Producer / Consumer examples, which are not exposed in Azure Functions, only KafkaOutput.

The examples I found basically say to use a propagator and an injection

private static readonly TextMapPropagator _propagator = Propagators.DefaultTextMapPropagator;
...
var contextHeader = new Headers();
var contextToInject = Activity.Current.Context;
_propagator.Inject(new PropagationContext(contextToInject, Baggage.Current), contextHeader, InjectTraceContextIntoHeader);
...
private void InjectTraceContextIntoHeader(Headers headers, string key, string value)
{
    try
    {
        headers.Add(key, Encoding.UTF8.GetBytes(value)); // adding as byte array
    }
    catch (Exception ex)
    {
        _logger.LogError(ex, "Failed to inject trace context.");
    }
}

How would I do this with Azure Functions? Where the first call of the Azure Function creates a Parent Trace, passes it on to the Kafka message and then a different Azure Function triggered by the Kafka message reads it and goes on with the trace?