Projecting is kind of a strong word.
On the contrary, I’m fairly confident these are just some of the most obvious, and there must be a ton more because I’m certainly not an anime expert, nor generally painstakingly step over every single frame analyzing the smallest details.
Some of those above are just small homages, like:
Macross / Robotech - Itano circus (this one is even explicitly mentioned in Amazon’s own X-Ray)
Tekkaman - Robot’s internal design, which reminds me, it always made me wonder why Robot’s face looks like a Samurai mask (or whatever the hell it is supposed to be)
Urusei Yatsura - Allen’s character design? I’m nowhere near 100% positive about this, my exposure to UY has been extremely limited.
Others are not so small, e.g. the obvious similarities between Cecil and Aramaki, the troopers’ design and use of optical camouflage.
What’s weird to me is that I would have expected someone to have already compiled some list of homages and connections, but there was none I could find. Maybe the TV show’s too new, yet.
Definitely looked that way to me (PPS: exhibit A), I assumed it was some kind of humor about (super-hero) stereotypes that I only got on the most superficial level, what with Eve at some point dropping a remark along the lines of “I’m the pink one after all”.
PS: But there is one thing that you could call ‘generic manga’ that I forgot about: Mark being an otaku of sorts AND having a box of tissues on his desk that are obviously meant for masturbation.
Mark is depicted to literally work to buy comics, of which he has a larger collection, is a huge fan of an obscure / ridiculous (as highlighted by William’s comments) comic (Seance Dog), apparently has had no relationships with women whatsoever, other than his mother, until basically he gets his powers – AND, when he finally gets on the phone with Amber, he stammers and embarrasses himself like the classic otaku stereotype.
I mean the supes are showbiz: the super hero system could be seen as a parody of the celebrity / star system (for lack of a better expression). I’d say most of the satire about the media that come to mind is American-made, but I don’t consume nearly enough British media to make any kind of accurate statements there
Sure, I have seen In the Loop but I haven’t had a chance to watch Veep yet.