So far it seems like they sort of vaguely want to turn Fortnite into it... but I haven't really seen much that I would call concrete.
I always thought their Travis Scott event was a pretty good example of something you could call early metaverse-ish, going beyond the usual scope of the game
https://www.youtube.com/watch?v=xG9-6k3RYIU
Slide 46 and on (mentioned on 48) is largely metaverse and a bunch of stuff presaging the Apple lawsuit, even though Fortnite hadn't launched yet:
https://cdn.akamai.steamstatic.com/apps/steamdevdays/slides2...
Of course that requires protocol interop (as did the Internet with TCP/IP and HTTP) and who knows if it will happen for the Metaverse.
I'm pretty sure that's not how they see it. I think the vision is of the singular Metaverse as the new narrow waist upon which all future apps are built.
I think it's been pretty clear that they're going to work on their own metaverse products. Epic seems to build on Fortnite , while Meta have Horizon.
I don't believe either have stated compatibility as a goal.
I know that the Web 3.0 Cryptocurrency crowd have ideas on the idea of a decentralized web with a shared ontological understanding, so maybe that's the source of the idea of there being a single metaverse?
But neither Epic nor Meta seem interested in a shared ecosystem. The metaverse is a product and their implementations will compete. I'm not sure if people would even want to be in two separate metaverses so competition will be fierce.
Most media (books/movie) sidestep that by usually having a single metaverse creator. That's in large part because it's narratively easier to deal with a single villain and universe. I don't know of any that posit having competing offerings.
The metaverses will be similar. They'll end up with many of the same apps and experiences, but devs will have to publish independently to each platform.
https://tech.fb.com/connect-2021-our-vision-for-the-metavers...
https://www.epicgames.com/site/en-US/news/announcing-a-1-bil...