Apache Druid

I thought this happens at the end of the ingestion task lifecycle, when the Supervisor tells the ingestion tasks to pause so it can reset "endpoints" to cause the tasks to finish their work immediately, build their last segments, and exit.

That's correct, and it also happens in the additional case of intermediate publishing (the task may continue to work after the publish)

Either way it's connected with the checkpoint/publish process

Typically, the pause is very short, like a few seconds. If it's longer then you may have some issue with your Overlord or metadata store