It would have to go through some sort of Lemmy link redirector service because a site can’t access another site’s cookies. And even then, with third-party cookie sandboxing, that still wouldn’t work.

I don’t think this is solvable without a browser extension. The best the devs could do is let you enter your home instance URL on each instance such that eventually you’ve configured them all and it works. But the extensions are just plain better.