Publisher does not automatically propagate otel baggage information when publishing event

[mroeha]

Is your feature request related to a problem? Please describe.
In version 1.133.0, java pubsub client already use OpenTelemetry. But after testing it, it does not automatically propagate baggage information. It only propagates traceparent information.

Describe the solution you'd like
Automatically propagate baggage information.

Describe alternatives you've considered
Automatically propagate context using registered propagators in open telemetry.

Additional context
Similar to how kafka auto instrumentation works, they use openTelemetry.getPropagators().getTextMapPropagator() to get the propagators and inject it using propagator().inject(context, record.headers(), SETTER);.
https://github.com/open-telemetry/opentelemetry-java-instrumentation/blob/e2dd703a8a0d47ed12d3beca79dc9740822da4f1/instrumentation/kafka/kafka-clients/kafka-clients-2.6/library/src/main/java/io/opentelemetry/instrumentation/kafkaclients/v2_6/KafkaTelemetry.java#L226

[michaelpri10]

Hello! Currently, across all languages, the Pub/Sub OpenTelemetry design uses the global propagator. In order to propagate baggage information, we would require allowing users to set their own composite propagators. We are considering this in the future, but do not have current plans to implement this. I would advise creating an issue at https://issuetracker.google.com/issues, so that other users may mark their interest in this as well. Thank you!