With short camper I see on the picture and empty water tank, I don't see how leaving the camper on its jack can create a problem.
My big camper start showing floor separation when I had it with lot of water in the tank, but at the time the water damage weaken the front wall.
Also if you have wood frame, check the angles between front lower wall and side overhangs.
My camper has aluminum skeleton, but all wood on that wall. When I come to repair the water damages at the bottom of the wall, I measured that overhangs sag well over an inch, due to camper sitting on its floor most of the time.
So when I was storing the camper- I used both - front floor support and jacks to keep it square. Did not worry about the rear, where I have strong aluminum bumper adding to structural integrity.