I’ve thought about it, but it’s not something I’ll be able to do anytime soon. If it was something like making the extension “official” or having a way to expose web accessible resources for the sites to use, that would be something I could try. Doing away with the extension entirely is harder.
Unfortunately I don’t know much about having a persistent cookie (with the home instance) that different sites can get from the browser, and I don’t know about another way to generate the links. That’s also something which might have privacy concerns if implemented poorly, because any site will have access your home instance (and whatever other information is required). A browser extension was easier to implement because thats something that’s meant to work with many sites, and everything happens locally on your device, so I was more comfortable publishing it.
Some of the other features, like the “trigger a search” button on the community not found page, or even just more instructions on what “community not found” means, those are changes that I can more easily push to the codebase. If it’s not already being worked on, then I’ll look into doing it myself :)