Will Trump vigorously pursuing death penalty affect Luigi Mangione's trial?

Legal experts believe the transition from President Joe Biden to President-elect Donald Trump would impact the Luigi Mangione case as Donald Trump condemned Biden's latest clemency and said he would vigorously pursue the death penalty from day one of his office. "As soon as I am inaugurated, I will direct the Justice Department to vigorously pursue the death penalty to protect American families and children from violent rapists, murderers, and monsters. We will be a Nation of Law and Order again!" Trump said.
Luigi Mangione is a murder accused who cold-bloodedly fired at UnitedHealthcare CEO Brian Thompson killing him on the spot. He has been charged with federal murder which makes him eligible for the death sentence. Apart from federal murder, he has been charged with first and second-degree murder and terror by the New York state government.
Luigi Mangione gained unbelievable stardom even before he was arrested as many social media users hailed the killer for avenging the death of many Americans who must have been denied their insurance payout by UnitedHealthcare. After Luigi Mangione was arrested, he became viral for his good looks, his Ivy League education and started receiving a huge amount of funds for his legal defense. The admiration reached such a point that his looks, his sweater, his perp walk in New York -- everything makes headlines.
What Donald Trump said on Luigi Mangione

Donald Trump did not say anything about Luigi Mangione or Brian Thompson per se but condemned the admiration he's been getting. "How people can like this guy, that's a sickness actually. It seems like there's a certain appetite for him. I don't get it.... It was cold-blooded, just a cold-blooded, horrible killing. That's very, very bad, especially the way that it was done."