Ok, so, my understanding is that self-hosting is running a web service for personal use. This isn't self-hosted. It's a Chrome extension. It's like saying that you're "self-hosting" Microsoft Word because you have a Word window open on your desktop. (Or, slightly more similar, you're "self-hosting" magit because you have emacs installed locally.)
IMO, selfhosting here was descriptive in that the Chrome extension is storing all data and generating all recommendations locally, without the use of a managed service that would presumably be storing all of my history in someone's cloud instance. (I'm sure you're a great person, OP, but I wouldn't want to give you my entire browser history.)
Yes, it's shipped in the Chrome web store, so OP could theoretically ship different code than what's showing in the open-source repo, but you actually _can_ selfhost even "further" by building the extension yourself (even if installing unsigned extensions in Chrome is harder than ever, I think it's still possible, and certainly Edge still allows it via Developer Mode).