I mean, Pych Up isn’t even a Psychic-Type move (it’a Normal-Type), so why should Rest be?
Possibly because the Rest definition is that the user falls asleep, which could be associated with Hypnotising itself into sleep, healing all its status.
Although no one outside of GameFreak can say for certain, one reason Rest could be a Psychic-Type move is because it makes the user fall asleep, allowing it to rest it's brain (with psychic power often being associated with the brain).
Hope I helped :)