You don't have two formats, though. Jj transparently works with git. I use it for everything and none of my collaborators is even aware that I'm using jj.
Maybe you feel that jj git fetch and jj git push are using "git" but it means you avoid the git cli in favour of the IMO better designed jj cli.
So, I claim that Jujutsu actually doesn’t work well with git repositories (and forges) very well, and I would like to see a native one.
The only issue is being in detached HEAD all the time, but in practice it's not a big problem for me.
Most of jj’s stuff is purely local. I woke on GitHub with jj just fine, the only thing people notice is that my autogenerated branch named are a bit odd.