To add to other answers, consider that when a 6kg animal lands or jumps on a shelf, the force can be double or more than their mass, and include sideways vector forces too (I asked a cat.)
Get shelf brackets, and try to locate a stud, at least one, to attach to. If you can’t screw into the walls no matter how minimally invasive, consider a storage unit that sits on the floor, one that looks like a group of geometric shapes (boxes.) Set thin shims under the front part on the floor so the unit leans into the wall slightly. It’ll be less likely to fall over that way. Again, double sided tape or surface gluing won’t last for long.