It's a pointless question. Antony was this expensive because United insisted on buying him late in the window when Ajax didn't want to cooperate - so there was a huge premium that had nothing to do with Antony's actual value (which anyway also depends on remaining contract length). Except if he becomes super good or United are dealing with a club in a similar situation, the price will never be the same.
That doesn't mean that United didn't overpay for Antony, but ultimately, that's United's fault, not Ten Hag's (or Antony's). He just shouldn't have to make those calls, United should have a structure for that and be much more proactive. (In fact, I think
@Adnan explained that United had a chance with Antony much earlier that window, but kept on waffling until that last-minute situation.) If that doesn't change within United, the next manager will end up making similar errors.
I mean, Ten Hag clearly doesn't seem to be a master transfer strategist, but which coach is? Klopp made some errors when he pulled more power to himself, I think Guardiola doesn't really want to be involved at all, and I am not aware of someone like De Zerbi ever having given signs of being good on transfers. (If anything, Ten Hag had some pedigree in that respect, as I think he was a de facto DoF at Utrecht - although obviously he's not shown he can play that role at the highest level.)
So yeah, that transfer was poor business, but it was the result of a poor process, and blaming (or even sacking) Ten Hag for being poor at a job he shouldn't have (if United's organization made sense) would be illogical.