Looking at his recent choices, Chalamet seems to be deliberately balancing his portfolio rather than running from anything. He's got two Dune films under his belt now, and jumping between massive franchises and smaller character-driven work is actually pretty smart strategy - it keeps him from being typecast and lets him work with different directors and storytelling styles. Plenty of actors at his level do this exact thing; it's not burnout, it's calculated career management.
The indie projects also get him critical attention in ways that blockbusters sometimes can't. A smaller film with a respected director can generate serious buzz in awards circles and among film enthusiasts, which is valuable currency even when you're already famous. Plus, those kinds of roles often let actors flex their range more - there's less studio interference, more time to develop a character, fewer explosions in the way of actual acting.
He's also just at an age where he can afford to be selective without worrying about his bankability. He doesn't need to prove himself anymore, so why not work with filmmakers he actually wants to collaborate with instead of just chasing the biggest paycheck or franchise installment? It's the opposite of a weird move - it's what someone does when they're confident enough to prioritize interesting work over obvious career progression.