For example in a tree, the water is lifted from the high concentration in the soil to the low concentration higher up in the tree. But at the end of that process the water has been elevated, which should take energy (=mgh), but it seems like it kind of gets lifted for free without spending any energy?
Similarly, dipping a paper towel into a bowl of water, the water “climbs” the towel (by capillary action?) and absorbs upwards, meaning the water was lifted upwards (so gained potential energy) seemingly for free?
Speaking only in terms of energy:
Molecules attract (adhesive and cohesive) causing capillary rise. Actually pottential energy due to that force is reduced converted to kinetic energy of motion which then gets converted into the gravitational potential energy mgh.
Now capillary rise won’t happen endlessly. It stops at a certain point where it cannot pull more water.
You could evaporate this water so that more water would flow up(also works in trees, but their mechanism of pulling water is more sphisticated). But now, on evaporating, you are applying more energy to it, which molecules held by adhesive and cohesive forces are puller apart, making it gain more potential energy to pull more water from bottom.
The reason why it rises is to minimise the potential energy and it does not increase energy