I'm curious what these services are using as a back-end, are there any free alternatives that they might be using, or are most of them proprietary?
More generally, upscaling is probably going to be >95% established algorithms with at best a small amount of perceptual heuristics to accommodate human vision. But I wouldn't expect perceptual heuristics to be common outside of tools like Photoshop because most of the time it won't matter and SEO is going to generate more revenue for a web service than quality.
I doubt there's much proprietary technology, it's understanding graphics sufficiently to make good judgements that's going to be rare.
The reason I ask is because it could be really useful for stuff like wallpaper resizing where the only thing you really want is for the larger size to look decent, not necessarily be exactly like the original.
I’ve barely used it so I’m not sure what to look for to figure this out on my own.
https://legacy.imagemagick.org/Usage/resize/#adaptive-resize
Be sure to scroll down to liquid rescale also.