Sway or deflection would come from the head tube area which is very stout. Rides like a regular bike if not a little harsh over big bumps (expansion joints, train tracks, curbs :)

edit as I just had a look at Tacx...
The P5X(and p3X) has the through-bolted axle. So my Tacx trainer, I would have to order a special part made for that hub size. Flux - my guess would need to be adapted which is something to check on with your LBS/Tacx.

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I don’t have a P3X, but I do have the P5X and have been riding at least 4-5 hrs a week on a Wahoo Kickr (original and 2018 version) and have had no issues. Initially, I noticed a creak when pedaling through harder intervals (I could never figure out if it was because of natural sway or not), but when I re-seated the thru axel a few weeks after setting it up, the creak went away - so, it was because I had the axel too loose. From what I have read and understand, the P3X is actually stiffer than the P5X and should actually “sway” less. Let me emphasize, though: if it does sway, it isn’t much. I’m 5’11” and ~170lbs and I never notice it. I don’t try to over-torque it while pedaling hard, but I also don’t worry about it. I can’t answer your questions directly, but I hope that some of this info helps. (I also have other tri bikes that I’ve trained on recently and over the years and the only difference that I notice between a traditional triangular frame and the P5X is on the road and there are so many other variables going on at that point that it is more complicated than just the beam tube design of the bike.)

Thank you for the reply - I’m just trying to figure out between a P3 and a P3X and that was one question that had lingered in my mind. Thank you - now just to make a decision