Presentation is a queue operation. That's why you submit it to a queue. A queue that will execute the presentation of the image. And specifically to a queue that is able to perform present operations.
As for how to synchronize... the specification is a bit ambiguous on this point.
Semaphores are definitely able to work; there's a specific callout for this:
Semaphores are not necessary for making the results of prior commands visible to the present:
Any writes to memory backing the images referenced by the pImageIndices and pSwapchains members of pPresentInfo, that are available before vkQueuePresentKHR is executed, are
automatically made visible to the read access performed by the presentation engine. This automatic visibility operation for an image happens-after the semaphore signal operation, and happens-before the presentation engine accesses the image.
While provisions are made for semaphores, there is no specific statement of other things. In particular, if you don't wait on a semaphore, it's not clear what "happens-after the semaphore signal operation" means, since no such signal operation happened.
Now, the API for vkQueuePresentKHR makes it clear that you don't need to provide a semaphore to wait on:
waitSemaphoreCount is the number of semaphores to wait for before issuing the present request.
The number may be zero.
One might thing that, as a queue operation, all prior synchronization on that queue would still affect presentation. For example, an external subpass dependency if you wrote to the swapchain image as an attachment. And it probably would... if not for one little problem.
See, synchronization is ultimately based on dependencies between stages. And presentation... doesn't have a stage. So while your source for the external dependency would be well-understood, it's not clear what destination stage would work. Even specifying the all-stages flag wouldn't necessarily work.
Does "not a stage" exist in the set of all stages?
In any case, it's best to just use a semaphore. You'll probably need one anyway, so just use that.