In a previous administration, a previous CEO of AccuWeather was appointed to run NOAA.
This is extremely common, since who better to run a weather forecasting organisation, than someone who previously ran a weather forecasting organisation.
If anything, that's evidence that even when Trump had ample opportunity to privatize NOAA, he didn't.
And yet, despite having all the levers to do so, Trump never privatized it.
Since you're conflating anecdotes with evidence, perhaps you should also consider the "evidence" that Trump has already decided not to do exactly what you're seemingly convinced he wants to do.
AccuWeather isn't a weather forecasting organisation. They merely provide an interface to data gathered by others.
Trump had zero opportunity to privatize NOAA because you can't do that via executive order furthermore that would be were it even true useless in discerning whether he or indeed others in his circle wanted to do that now.
It doesn't take more than three seconds of Googling to get your answer. No wonder American media literacy is at an all-time low.