No. You don't stay logged in when you go there.

Right now, I can click along the top of the page on Lemmy.World "communities. If I do, it takes me to a list of all the communities on Lemmy.World.

I can't go to another instance directly, and click communities while also being signed in. I can search for other communities on other instances, but I can't get a list of communities while signed in.

I should be able to go to Lemmy.Zip, and it should route me to something like Lemmy.World/Lemmy.zip so I'm viewing Lemmy.zip while still signed into Lemmy.World.

That way you can browse other instances communities and just hit subscribe without having to do the extra work of copying !community@instance.domain then going BACK to Lemmy.World, searching for !community@instance.domain, clicking the search result, and THEN you're inside the community while still signed in.

It would save several steps, plus retain my settings as I do it, and make Lemmy seem like a more seamless experience. Rather than a hodgepodge of various patched together pieces cosplaying as a website.