Where I'll give Brady the edge on the mental side of the game comes from watching the Patriots retool their offensive systems many times and seeing Brady perform well in each of them.
Now, I don't think Mahomes is incapable of the same thing, but he's not had to go through it yet. He probably will fairly soon when the Chiefs start to see their skilled players move on to other teams due to cap limits. New players will be brought in, which will change up how they have to play.
Biggest adjustment for Mahomes will be when he cannot throw side-arm perfect spirals 50 yards down the field... and depending if he is lucky or not, it could be 5-6 years down the line... which in terms of his whole career is pretty soon (and could be sooner if he, God forbids, gets hurt). His mechanics are not easy on the body and he'll have to adjust them to remain dominant. That's when he'll need to be able to show mastery of the mental aspect of QBing.
Losing skill players will hurt, but not as much. As long as Mahomes can extend the play a few seconds and throw it like he does right now, guys will have enough time to get open down the field. Hell, the Chiefs should invest in a great OL before they invest in keeping their skill guys.
He should have plenty of time to adjust and he seems like a smart kid, so I think he will, but yeah, that's gonna be his biggest challenge. That's why Manning and Brady were good for so long. They biggest strength is their mastery of their offense and their ability to read the defenses in front of them. If Mahomes develops that, still can move around AND adjusts his throwing mechanics as he ages, he should be able to have at least as great a career as them. Might not be able to match Brady is rings and post-season accomplishment, but he can beat the stats and have an overall "better" career.