> if someone claims that black swans existed, and someone else is skeptical, the onus is on the pro-black-swan side to provide evidence

Your example is exactly backwards. Black swan events are meaningful because they don't have prior evidence to inform their existence. This is the opposite of the case for zoonotic spillover - there is a well established pattern that should be present and is not.

Actually, your point is unintentionally correct - the black swan event here would be if zoonotic spillover DID occur, because there is substantial, expected, historically modeled, missing evidence. So, as you say, the onus is not on the lab-leak believer.