In order to be able to assert the outcome of some actions, API integration tests need to be able to cause the job queue to process all pending jobs. This can be done via the internal Special:RunJobs endpoint.
This serves a similar purpose as T230211: Enable API integration tests to ensure that GET requests will always see the effect of previous POST requests., but is technically orthogonal. During testing, most tests should probably wait for DB replication, but most tests don't care about the job queue.
On the other hand, the test suite should not leave the target wiki with a large number of unprocessed jobs either. We may want to provide a way to truncate the job queue as well, maybe using a maintenance script.