So basically, software and console side, HDR means the brightness level now goes from "0" to "2" where "1" is the brightest that older monitors could go.
Upscaling to 4k just copies and adds pixels next to existing pixel to make the image bigger. Sometimes upscalling makes the image look worse even. blurry.
Upscaling sometimes resamples images. It's just just a "closest neighbour and then some" duplicating, you have directional gradients, multidirectional gradients, all sortsa bullshit.