Huh, i thought ps5 (pro) was 4k native, but looks like its via some hardware upscaler. Good to know hehe. That changes some things, but lets see. The ps5 pro gpu is equivalent to a rx 7700 xt, which is a 400 msrp card. In reality its way more, but lets work with msrp prices to give this the best chance of success.
Ps5 pro is 700$ msrp, so thats 300$ you have left for cpu, ram, ssd, case, and psu. I dont think you can do that, but lets look at the next part: cpu
Cpu is equivalent to a ryzen 7 3700x, which is an old cpu so is cheap atm, 120$.
Ok, 180$ left in the budget, next: motherboard.
I found a board on amazon for 65$, which was the ASRock A520M-HDV. 120$ left.
Ok so, ssd. Ps5 pro comes with a 2TB ssd. I found some sketchy, offbrand, m.2 ssd's from brands i never even heard off for 94$. There is probably cheaper, but amazon's website was being an arse and lets face it, how trustworthy or slow are those. 36$ left in budget.

Thats 36 for ram, case and psu... As much as i hate to admit it, as a pc person, you cant make a pc with equal strength as ps5 pro and it sucks arse.
Second hand might give us more leeway but i dont think its a lot.
I will agree that yes, with pc you have a lot more options and its easier to put in a bit more into the budget to build a way better pc than a ps5 pro.
But from a pure budget standpoint, no pc isnt worth it.
As soon as you add other arguments, the choice changes