It doesn’t seem that Giuliani was acting in any government capacity at the time. Regardless, even if he was, he did not engage in any search or seizure. The hard drive was turned over to him voluntarily by the laptop repair guy. Evidence seized by private actors like the laptop guy, even illegally, is not subject to the exclusionary rule.
I hope you’re right. I remember a few NY case rulings that make me doubt. Not my field anymore, though. I’m glad the NY Post got it.