Let's say, hypothetically, that the president was taking tariff revenue and transferring it into a Trump-owned bank account rather than into the Treasury. Yeah, you'd have to prove it. But that would absolutely be outside the scope of his legitimate presidential power.
In real life, it wouldn't be that simple. There would be a veil of plausibility, and so it would be harder to prove. But I claim that he can still be prosecuted. He has the presumption that what he does is within the scope of his office; the burden of proof is very much on the prosecution. But he does not have complete immunity.
Complete, no. But the combination of the expansive powers given to him by the court, and the difficulties of burden of proof, means that it's hard to imagine him being successfully prosecuted for just about anything.
I think that includes persecution of political opponents. Maybe not for a capital offense, though I wouldn't be so sure. Treason is poorly defined and has capital consequences.
In real life, it wouldn't be that simple. There would be a veil of plausibility, and so it would be harder to prove. But I claim that he can still be prosecuted. He has the presumption that what he does is within the scope of his office; the burden of proof is very much on the prosecution. But he does not have complete immunity.