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I am not convinced there will be any public betas. 13.4.5 is a long term project and once installed would stop a member of the public from receiving a 13.4.2 or .3 or .4 update.
It shouldn't matter, if 13.4.2, .3 and .4 updates don't have betas (as 13.4.1 didn't).
 
They have an app already. https://www.apple.com/newsroom/2020...vid-19-app-and-website-based-on-CDC-guidance/

But I don't see them building into iOS.
That’s a completely different app.

First will come the tracing app in mid-May, then it will come as an iOS update in the months after so the app is not needed.

 
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