I only played Jumping Flash! one time at my cousin’s house. I didn’t come into possession of a Playstation console until several years afterward and had, by that time, nearly forgotten everything about it.
I never bothered to find out what the story was or what my motivation was, but I do remember that you see the action through the cockpit of a rabbit-shaped robot as you use your ludicrous jumping ability to collect things around a variety of stages.
I guess I just remember this game because it was such an early 3D game that developers didn’t know what to do. A lot of those early games just had landmasses floating in the air for no real reason and weirdness for the sake of weirdness. This game at least tried to make it fun, and it was oddly compelling. And it made me want to pilot a giant rabbit robot. Which still makes my shake my head when I think about it.