Do u think mario and Luigi act like each other as a response to trauma?
I don't think so, but i do think that they...
Pick up on a lot of each other's habits by virtue of being brothers who lived their entire lives together
Find each other to be inspiring in their own special way
Luigi has a strong desire to be brave like his brother. He pushes his own boundaries while following after him, and exhibits shame in his inability to defend himself.
Meanwhile, we can see that Mario makes a conscious effort to play it safe and keep his mouth shut much the way Luigi does... even though Mario often ends up caving to his own bullheaded determination in the end.
I think instances where they act like each other are less a trauma response and more an effort to self-comfort and find balance.
Mario definitely went through MORE, but not all of it was bad; he fell in love with a beautiful realm, made lifelong friends, and had the quality he was always shamed for praised at last. Luigi went through a smaller quantity of tribulations, but the whole thing was tinged in idleness and hopelessness. Even though DK and Peach warmly accepted Luigi at the end of the movie, Mario was the one who earned that friendship. Part of the Weeg angst potential could be him feeling like Mario blossomed into the person he was always meant to be while Luigi wasn't there to see it and cheer him on, and he feels like he can't keep up.
Also there's the fact that Luigi was already struggling to keep up with his brother when they were just plumbers, so while he no doubt feels happy for Mario I definitely think there would also be a sense of loss that he and Mario didn't get to grow together.
They had never been apart that long before, and it's just Luigi's luck that in the span of time that they were separated Mario learned all about the surrounding kingdoms, powerups and how to use them, how to fight and drive motorized war karts, and much more.
So if Luigi felt like he was falling behind before, I'm willing to bet he now feels completely left in the dust.
Even though they defeated Bowser together I imagine that once the high of that victory wears off, Luigi would be left with a strong sense of imposter syndrome.
Sure, he saved Mario with a manhole cover... anyone would do the same. Everything after that he only managed to do with the power of the super star.
In the first movie Mario struggled with being perceived as a joke and wanting to prove everyone wrong, so I think it would be interesting if Luigi spent the sequel believing himself to be a joke and wanting to fix himself, even if it means pushing himself too hard and following his brother into dangers he is not physically/emotionally ready for.