Several media organizations (washington post, buzzfeed) submitted FOIA requests for the emails, and as per federal law, they were released. No leak, normal federal government policy process, driven by mainstream-y media outlets AFAICT.
Twitter has not banned discussion of the theory. Here's a thread from May 27th (Nate Silver) discussing it in some detail:
https://twitter.com/natesilver538/status/1397869883585708034
Here's Ryan Delk from May 23rd saying it even more clearly:
https://twitter.com/delk/status/1396583148524212226
They did have policies related to the lab leak theory, but it seems like a mischaracterization to say that the banned discussion of it.
The only person I can find who has lost their account over related matters is a NY Times reporter who closed her own account after making some fairly dumb remarks about the theory.