How do I do that from the web browser version of lemmy.world?
I try going to that site and can't subscribe unless I'm a member of masto.ai. If I search for user on lemmy I find him, but there's no obvious subscribe mechanism.
You won’t, the format doesn’t really work well together. You can technically do some interactions between them, but there is no client that makes it easy for you.
Don’t stress about it. Just think of them as separate.
Kbin doesn’t have an API yet, so most app developers don’t go for it, the only one I know of is Artemis, but that one doesn’t support Lemmy yet (it is planned).