The best platformer games like Psychonauts are Psychonauts 2, A Hat in Time and Super Mario Odyssey. Below are 7, each with the reason it is here — and, at the end, what filtering to platformer costs you.
Filtering to platformer means you want the movement itself to be the pleasure. It is the right filter when the thing you liked was getting from one place to another.
What you get: A game you can judge in ten seconds. Platformers live or die on the jump, and a good one feels right before anything else happens.
What made Psychonauts worth playing in the first place is covered on the full list. This page is the platformer part of that answer, and only the platformer part.
Everything the first did, with controls that finally match the ideas.
The closest indie game in tone and structure.
For the one-new-idea-per-level design at its best.
The other comedy platformer worth playing for the writing.
The collectathon Psychonauts is built on.
Every chapter is a completely new mechanic, and it is superb.
Same generation, same open platforming, harder edge.
Weight. Platformers rarely carry a story you will think about afterwards, and the collectible-led ones can become checklists if you let them.
Specifically, these are strong answers for Psychonauts that are not platformer games, so they are not on this page:
The full list is on games like Psychonauts — 9 picks, no genre filter.
Psychonauts 2. Everything the first did, with controls that finally match the ideas.
No. Psychonauts released on the Microsoft Xbox, but a recommendation is only useful if you can play it, so the picks above span platforms and eras. What they share is the genre and the reason.
Whether the move set is complete early. The great ones give you everything in the first level and spend the rest asking better questions of it; the weak ones drip-feed abilities to disguise thin level design.
Different games. 2D platformers are about precision on a single screen; 3D ones are about reading space and camera. Each pick below says which it is.
By hand. Each pick was written for the full Psychonauts list first, on what the game actually does, and this page is the part of that list that is platformer — never a genre tag lookup, which is how "best racing games like Super Mario 64" used to be a page on this site.
Or read the platformer guide for where to start in the genre generally.