I got my 4k 60Hz monitor in 2017 for $400 or so. You can get them for $250 these days, so I agree that is pretty mid-range by now - or even the lower part of it. That leaves $750 for the computer.
According to the logicalincrements linked above, that gets you a RX 6600 - which they rate for 40 FPS @ 4k in The Witcher 3 - a game which came it out 2015.
So no, you cannot get a decent 4k monitor and a PC able to drive it for less than 1k. That's the entire problem: there is no midrange anymore.