There are plenty of proprietary online resources for image upscaling, and they seem to do a decent job, especially for paintings or drawn content: examples include bigjpg.com, icons8.com etc.
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.