Can a film maker or podcaster who make, write, research historical films, documentaries, podcasts....and are paid, some very handsomely, be considered historians?
Usually not. There's a reason why the History Channel barely has any history and is mostly UFO intrigue, and that's because history doesn't pay. Podcasters get paid handsomely for being shocking and entertaining; what the plebs like you want to see. Cooper's fans wait with bated breath for the dog whistle, for those not-so-cryptic lines loud and clear to them as pro-Hitler, whether or not it's because they are ideologically bent that way or just like the lols. Tucker likely doesn't have any horse in the race beyond shock and clicks. He likely doesn't think Cooper is the world's greatest historian (or even a historian) and just said that stuff to rock the boat.
People who make films about history are usually called documentarians. A good documentary will consult good historians. Your example of Foote as a non-credentialed historian is one of those borderline cases. From wiki, he was already a professional writer, which puts his foot in the door for taking on the project Random House (a credible outlet) pitched to him. He self-described as, "Foote described himself as a "novelist-historian" who employed "the historian’s standards without his paraphernalia," some of that paraphernalia he lacked got him criticism for limited sources and "Academic historians routinely lament Foote's lack of citations."
So the question about whether or not he achieved historian status would be the extent to which other historians cite his work. He definitely made it as a history popularizer...but? History isn't like the natural sciences where if somebody forgot how to do an experiment it can be re-remembered. In history, once a source is gone its gone. Provenance is everything. So if he's a great writer and storyteller and even if he more or less got his facts straight, all that blows away if his sources and citations aren't dead reliable, or if he didn't carefully articulate his sources. As a historian proper, it's less about how many people will read the book and learn something even if it's accurate, and more about how many historians will use his book to further their own research.
Cooper isn't even up for consideration. The answer is "no" without further ado. He's a rabble rouser with an interest in history. He studies history in order to offer politically charged opinions and interpret world events to the liking of right-wingers. I like Peter Zeihan as a geo-politics guy. He's written several books that require considerable knowledge of world history, he'd wipe the floor with Cooper any day of the week in terms of knowledge of history, but he's not a historian. I have a friend from years ago who was an amateur history buff with a photographic memory. He could cite endless historical trivia and when he decided to get some college credits he walked in a tested out of any history class they'd allow him to do it with. But, until you've produced that paper or book with uniquely reliable content that future researches will cite rather than citing something else, then probably not a historian.
"if you can't admire Joe Biden as a person then it's probably, you got a problem." -- Lindsey Graham