Most of the "left-leaning" organizations you cite above are not considered particularly left-leaning by the left. A better description of them would be "pro status quo", or if you're feeling punchy "relentlessly pro status quo" with a side of "pro-corporatist" thrown in for seasoning.

Now, Fox News and OAN and Sinclair are not, publically, actually the John Birch Society, so sure, you could say "right wingers don't think they lean right either".

Plot out a chart of US political opinion, and I more or less guarantee you that in most things, you'll find your list of media outlights absolutely "centrist", and the 3 I just named distinctly "to the right" of mainstream US political opinion.