I do not understand how these two ideas are somehow different (and I even say that as someone who thinks caring about star counts is harmful to both sides): if there were a way to track/surveil how many users had bookmarked your website in their browser, it seems like it would be a sane and even rational (if also annoying and harmful and short-termist) thing to use that as a signal on both sides, to both optimize for as a website as well as as a potential user to judge the popular interest in a website... it certainly is a shitty heuristic, but
even I will admit that,
usually, a website that is bookmarked by a billion users is likely more "important" than one that is bookmarked by only a few users?
But like, any indirect signal, by its very nature, both can be gamed and will be gamed once people care about it, and so you need to be extremely careful ever using such signals on an ongoing basis, certainly once too many people know about them; and, frankly, if you make such a website, you should be doing everything in your power to prevent such signals from existing in the first place (such as by not tracking what users bookmark in the first place; or, if you somehow must, then keeping that information to yourself and not exposing it to users... this is hard to have fortitude on, as it also requires not trying to use it yourself as a signal, as people will figure that out and optimize for it even if they can't see it).