Well. Firing squad because it's a court martial sentence. Last deaths by firing squad in the States were 2025. Lethal injection isn't look too reliable right about now.
As for the live streaming, until 1868 Britain routinely hung people in front of baying crowds. In theory, this was to act as a deterrent. Also to demonstrate the long arm of the law. And we do see streams of people being executed in the USA, it's just usually they're young, black men and the executioners are the police. Perhaps public state sanctioned execution has become normalised for Americans.