That kind of explains why your dialogue seems targeted at a younger audience, both ATLA and Teen Titans, though excellent and appreciated by adult audiences, are targeted at teens and tweens, the characters are actually children and teenagers for the most part. RWBY is also mostly targeted at teens and not a great inspo for writing, RWBY's writers aren't experienced and were cribbing from ATLA and multiple other anime. If you take any inspo from RWBY, let it be from the fight choreo which is excellent in almost all cases, but the writing is generally not great and sometimes abysmal.
What reminded me of the MCU and Supernatural was the "bantery" type stuff, like the "he has a point" "shut up" and the other times there's two characters who care about eachother but don't want to admit they care about eachother, it's kind of thor/loki vibes and not something adults, especially older adults do because most people are just comfortable about saying they appreciate their friends and colleagues if it's true for example.
As for distinct voices, I'm not really getting that sorry, I can't tell who's talking just by the lines and I'm not entirely sure what the dynamic between the characters is, but that's also because it seems you've taken clips from many many scenes rather than just put up a short introductory paragraph or something. (I'm not saying you should do that, I'm saying that could bias the result).
But again if you're not specifically aiming for adult media and want to go more action cartoon comic YA, this could be a stylistic choice you can work on and innovate with, just making sure that you're aiming for that teen to early college-age young adult audience.
You've said you'd feel self-conscious writing dialogue like that, and that's sort of the point of writing. Writing involves laying bare a part of yourself, what you find normal, cool, uncool, good, bad, noteworthy, interesting, and trying to have characters that also have totally different perspectives from you and understanding them on a personnal level. Some really raw and emotionnal scenes hurt, because they'll connect to your own hurt. "Being cool" usually comes from having confidence in who you are and knowing what you like and don't and being secure in how people see you, even if sometimes they don't get it right first try. People who are edgy and immature and "trying to be cool" don't have a strong sense of who they are, and that goes for characters too. People can tell if you're trying too hard and it feels fake and like you're trying to get them to see you a certain way instead of just being a certain way and letting them see and decide for themselves how you are.
Levi Ackerman in Attack on titan is a "cool character" archetype, and says a lot of very edgy things. A lot of people make the mistake of only seeing the surface level of what he says and does and tragic backstory and blablabla, so when they get inspired by him to make a "cool character" they make a superstrong badass one liner spouting type who saves the day and then broods because he doesn't care about anything. They don't get that behind that Levi is a very consistent character. He is strong because there was a time he didn't have control and now he craves it, and that includes excessive cleaning of his environment. He cares very deeply about the people around him and that's what contrasts with his detached no-empathy type training he has for someone he sees as a tool to end suffering. He has a moral code and listens to characters he trusts, and sometimes he's right to, sometimes he's wrong to, and ESPECIALLY IMPORTANT the characters around him react naturally: they see he's strong but they don't think he's cool at first, they think he's an arsehole and treat him as such.
