The Galilean relativity principle is old physics but still more than correct enough for use in this type of situation. This states that the laws of physics are the same in in all inertial frames of reference.

So there is no fundamental physical difference between maintaining a position on an escalator that moves steadily downwards, and climbing stairs at a steady pace. The mechanical work you have to do is exactly the same.

Imagine you were walking up the stairs in a narrow stairway with smooth walls. And imagine there are walls behind you and in front of you that always stay at the same distance. There is no experiment you could do to tell the difference between a stationary staircase with motorized walls in front and behind, and a moving staircase with stationary walls.

To deal with your question about energy - you are converting your internal energy into potential energy in either case, in the same quantity. It's just that on fixed stairs the potential energy builds up in your body. On moving stairs the potential energy is removed by the device at the same rate that you add it. In the latter case the energy could in principle be used to power a machine attached to the stairs.