There was a lot of discussion about it during the transition (including this NBC News piece). And there are a variety of regulations on it. See, e.g., 31 C.F.R. 2.2. I don't think any of them say that a former vice president can retain documents in his garage. But I'm not at all clear that the law prohibits it.
So that's the actus reus. Then there's also the mens rea.
Unlike others who have clearance, former presidents and vice presidents aren't "read out" when they leave office. For other people, you get read out--a process during which you sign a statement saying that you aren't retaining any classified material and that you understanding that doing so would violate the Espionage Act. That signature provides evidence of the mens rea if it later comes out that you did, in fact, retain documents.
Without that kind of evidence, it'd be really hard to prove that Biden "willfully" retained national security secrets.