I can’t see what you’re referring to in those low-res images, but I’ve been working with jpeg for 25 years and have never seen “artifacts” magically appear in solid areas other than directly adjacent the edges of shapes, which can be controlled with image quality settings if needed. The encoding of jpeg does not introduce random content in solid areas. If it did, high quality photographs would look terrible.
I use jpeg almost exclusively for raster on the GF and it doesn’t introduce random dots either. It takes a clean image and engraves just what’s there. The only reason I might use a png if if the source is already in that format, or it’s from a screenshot (png is the default format.)
If the empty space around your image is in fact not empty, and has random pixels that are even 1 level above empty, that would cause issues like what you are seeing. You have to manually erase everything around a shape to ensure there is nothing there. That’s where I spend a lot of time when working with images from sources other than my own.