You put a sponge on a wet surface, it pulls water up against gravity. Where does the energy come from that now is kinetic energy in the water?
So I’ll use trees as an example.
Trees absorb water from their roots and use capillary action to push the water up its stem to its leaves. The reason water has energy is due to the surface tension between the water molecules with themselves and the tubes of cellulose in the tree. Water is then evaporated at the leaves bringing up more water in the process.
Molecules are kinda like magnets in way. They love to stick to some but hate to stick to others. This force creates the energy you are referring to.
Here’s a great read about it more in depth if you are interested: http://www.davidlnelson.md/Cazadero/Trees&CapillaryAction.htm
Sponges don’t use capillary action. They draw water in as they regain their shape. If you put a sponge on a puddle, not much will happen, but if you squeeze it first and then let it expand while it sits in the puddle, it soaks it up.
Intermolecular attraction. A bit like surface tension, except the water molecules are attracted to other molecules than each other. Being stuck to the surface is a lower energy state, just like magnets being stuck to iron are. You need energy to separate them again.