Why do the figures assigned as personas to the main characters always get this sort of high-tech, Cyberpunk look to them? Rather, why are they the only personae in their respective games to get this treatment? It just looks out of place when you as the player character swap out your initial persona for another one and it's of a more traditional design (well, traditional as far as mythical creatures and figures appearing int Atlus games are concerned) next to all these futuristic-looking entities based on mythical figures that your allies have.
I think it's just to show those particular Personas are unique to each of those characters. Compare Yukari's Isis with P4's Isis which does use the SMT Kaneko design. Also, using the latter for the MC's stock of Personas only really happened starting Persona 3. In Persona 1 and 2, most of the available Personas have art unique to the series (a few exceptions like Cerberus and Innocent Sin's Nezha/Nata Taishi). For example, this was how Shiva was designed in Persona 1 and 2, and he wasn't a signature Persona either◊.
Besides that, given how similar the premise is for the series' powers, I think it's safe to say that the Jojo's Bizarre Adventure had a big influence on the design aesthetic of the personas of the main cast. The shift is most obvious for personas based on figures that already had SMT designs to differentiate them, but the design philosophy is still present for others.
Is the apparent superhuman strength and agility demonstrated by Persona users the result of whichever cognitive world they're in or Charles Atlas Superpower?
Both to an extent. A Persona user's base abilities are dependent on the cognition of themselves and the public. The Phantom Thieves, for example, all display superhuman speed, strength, agility, endurance, and coordination regardless of their normal fitness because that is what the public subconsciously associates with the idea of a phantom thief. A Persona user's own cognition also impacts their abilities. What they feel makes them strong really does give them strength in the cognitive worlds. Most of the P4 cast wield a variety of random things as weapons. Despite almost none of them having any real skill with them, they're still effective in battle as the trained fighters in SEES because of this effect.
On the physical side, cognition only goes so far. The public's views of how things "should" go is often heavily distorted by media or personal ignorance, so the limits this can impose are often very inconsistent and arbitrary. So a Persona user still needs to practice and train in the mental and physical worlds to improve themselves in a more consistent way. Their base level of physical fitness and other skills have a noticeable impact on their performance in the cognitive realms which is why exercise and practicing in the real world are very important for their activities.