I would suggest keeping the edits light. Also look at the old display referred modules as they are well suited for JPGs who’s look is baked in.
The levels control or the RGB curves (sorry if I got the name wrong) are worth a try. Sorting out your black and white point and perhaps tweaking contrast can help a lot.
I don’t think there is any input upscaling, so perhaps use another app to upscale the image before processing, then you might get away with a little sharpening.