It cannot be dismissed as mere "correlation". These studies have been carried out on people of middle-class background too. Esp children of defense service personnel who have experienced frequent mobility. And studies carried out by different nations AND different cultures as well! Mental well-being is not mathematics - you cannot proof a definite cause with utterly no ambiguity.
Unfortunately, you took one single "could be" sentence out of an entire gamut of data confirming mobility-related mental health issues in children and completely ignored the conclusions section in that same paper, so I think you have already severely hardened your position and are unlikely to be convinced by anything I offer.
I would suggest simply talking to a practicing psychologist about this - you would probably be far more convinced than a HN commenter. Actually, this is where I first found out the same - I didn't know about this until a consultation with a psychologist.
(You can also ask your AI buddies - ChatGPT also confirmed it with several case studies offered.)