It is possible to clone:
the sprint-ID (This will associate the cloned issue to the same sprint.)
create a new sprint with identical name in the target project (This will create a new sprint and associate the cloned issue to the new sprint.)
You just have to select “Sprint” and the desired outcome in the Deep Clone dialog.
Deep Clone clones only open sprints (active or future). Completed sprints are ignored.
Sprints can be visible on several company-managed (classic) boards, depending on your board filter.
In team-managed (next-gen) projects sprints are only visible on the “Origin board”.