Hello @ktpn ,
Thank you for the follow-up and additional details!
One point to clarify - the HiveMQ Broker does not append timestamps to messages when submitting a message from the HiveMQ Broker to a subscribing client. That said, the Paho client library does generate a timestamp, though this is done outside of the broker.
If using MQTT5, one way to implement a timestamp that would be traceable through the entire pipeline (i.e. from publish, to the broker, and then to subscribing client) would be to submit the timestamp of the publish with a custom user property. More info on that can be found here.
Additionally, another user had a similar questions here on the community forum, and there may be further insights in the aforementioned thread, linked here.
Best,
Aaron from the HiveMQ Team