The actual quote:
Mainstream AKA leftist media [...tends to still support the War in Ukraine, etc]
Mainstream (aka leftist) media, is how that parses, for me. If you meant otherwise, you
really wrote that wrong. (No worries, we all occasionally do that.) As put, though, the implication there is that all mainstream media is leftist. (It is, of course, for the batshit rightwingers; much as the same entities are entirely the voice of the right-wing establishment for other types with the opposite and likely equally crazy philosophy. But you still don't seem to me to be
so far away from the middle-ground that you can claim that perspective.)
Much apart from my point that "leftist" does not map over "left-inclined", which I'll let slide due to overton windowing, Fox is (barely, perhaps) mainstream even while not being left(ist/ish/whatever). I would not exclude them from mainstreamness for being right-leaning, though they have perhaps significantly strayed from being 'media' on a number of occasions when the tail has done too much to wag the dog. Mainstream is a
spread, not a singular global message. And, whether or not the centre-of-mainstream is off-centre as far as any perceived viewpoint, it's a broad church that necessarily has room to span across matters that are off-centre in both(/all, technically) directions.
And I think Fox has
aspired to be mainstream, since its 'edgy' days of talking of "Leftist Mainstream Media" (which is a different meaning from "Mainstream Leftist Media", and both different from what you said). They certainly desire to be the "mainstream media for the right", but perceived failings in this regard have been taken advantage of by the likes of Breitbart News or NewsMax, by my understanding (which are way beyond my usual sources for neas/comment, most of the time, so I'm not sure where they are now).