I think the thing that distinguishes a 'pure platformer' from a more action/platformer like Ratchet and perhaps even Astrobot is that the toolkit you develop is focussed primarily on jumping.
Consider Odyssey - Mario has the single jump, longer jump, triple jump, reverse jump, stomp into a higher jump, ground cap jump, jump into cap toss into lunge and, finally, a wall jump. There really aren't many games beside Mario that place jumping and the rhythm around jumping at the core of the game.
Ratchet doesn't do that at all. You jump, hover and dash. The movement of your character owes more to third person action games.
Astrobot sits between the two, but for me, is still closer to a third person action game than one which focuses on jumping and movement.