There are points I agree with, and there are points I fail to reconcile.
Application of a force over distance transfers ("absorbs") energy.
Ok. Or, consumes energy?
Application of a force to an object that does not move (hardpack on a mountain) does not transfer kinetic energy from the skier, but it does change the skier's velocity.
I assume be “skier’s velocity” you mean the COM’s velocity. If that is correct, I am referring to a skier whose COM is going literally straight down, with skis carving turns on either side. There is no change of “skier’s velocity”, no change of COM velocity, velocity being speed and direction. The comparison I make is between a skier that makes no turns and straightlines and a skier that makes perfectly carved turns, ones that do not result in COM alternatively going at higher and lower speed (still in only one direction, down). In my mind, the skier making turns is allocating or diverting or consuming kinetic energy to facilitate the skis turning. Without forward motion (energy) the skis can’t turn
One way to think about this is a ball connected to a peg with a string (so that it's able to rotate freely around that peg). Give it a spin, and absent friction, it will keep moving forever even though its velocity is constantly changing. (If the highlighted quote were correct, the ball would stop after traveling 90° around the peg.) Satellites in orbit are another example.
I see that. However, the visual model I have, even if not correct from a physics pint of view, is that of an electric vehicle’s regenerative braking system. A flywheel, I think, slows the car down while turning a generator to charge a battery. When we ski, we turn skis instead of a flywheel, thereby transfer energy and reduce our COM’s speed. Where this analogy breaks down is energy from a flywheel gets stored in a battery. There is conservation of energy, though some is “lost” to heat. In skiing, I don’t know where the energy derived from slowing the COM (slowing the car) goes. I think that’s where you’re saying my model breaks down. But, setting real physics aside, the model does give me something that fits a lot of observations. More rapid turns, having same completeness, slow me down more. More complete turns, requiring more turning (acceleration of ski’s) slow me down more.
It is true that in this case, the portion of your velocity moving towards your suddenly-engaged edges must, in that moment, go somewhere. (Just like the ball isn't going to travel through the wall.) On skis, you're going to lose a lot of it to a combination of sliding (if you don't actually get the edges set immediately) and absorption within your body.
In my model, COM does not go towards edges. COM goes downhill. Skis, when turning, go toward COM in a carved turn. No sliding.
In a perfect carve, you're always moving in the direction your skis are pointing. The force you feel is the force required to change your velocity, but, from the reference frame of the "immovable" Earth (which is the frame from which we're measuring speed), your kinetic energy does not change due to the turn itself.
In a perfect carve, I feel I am always moving downhill, not in the direction my skis are pointing, except at the belly of each turn, where the skis are pointed downhill