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?
As others have stated, water in trees gets up thanks to two processes. The first is indeed capillary action. The tubes carrying the water are rather thin, and it clings to the sides of it. But this is a rather small part of the total energy carrying the water. The main mechanism is a negative pressure inside the vascular system of the tree. Basically, tree leaves sweat water all the time (more or less depending on temperature). The water leaving the tree kind of sucks up the water following inside the vessels (this is a simplification to not go into the physics behind). In some larger trees, the negative pressure inside the vascular system can be exceptionally strong, requiring exceptional strength of the tree’s components.