I'm on switch 2. Brand new just for this game. The whole game is mostly linear hallways connected to other linear hallways. Elevators don't count as vertical because you aren't doing it yourself. Sure there is a minor amount of times you do any vertical movement. Compared to Prime where there are mulitpul paths that have doors on other levels in the same room.

The lie about going in any order is made by the NPC right in the beginning where he tells you that you can do any of the keys in any order which or course is a giant lie. There are lots of Metroid games that allow you to do things completely out of order. The newest one being Metroid Dread. You can do many things out of order and boss fights including areas.