This is intended to work so that the aerial and aquatic supertypes can return a mana value card to put out a higher mana value one. However, I don't know if supertypes count as a card type. If they do not, I'd be willing to just sighs simplify this to just "creature."

The word "type" here is ambiguous. As written, it's implied you mean (creature sub)type, as in Soldier, Beast, etc.

I'd rewrite as such: "Each player who returned a creature to their hand this way may put a creature card of the same that shares a supertype with it, and with a greater mana value from their hand onto the battlefield. (Aerial and Aquatic are supertypes)"

There's probably a way to merge this second sentence with the first one to avoid repetition and make it shorter, dunno.

you forgot to remove "of the same".

"greater mana value" is open towards the top, which is not usually a restriction you would see. The design seems "dirty" tome in the way it seems to aim at giving you a restricted Show and Tell or Dramatic Entrance, but also uses the "drawback" of allowing the same to an opponent, except there are a lot of cases where itdoesn't work for them.

Why not simply "with a different name" rather than "with a greater mana value"? What is the grand plan on getting the opponent on board anyway? What about creatures without supertypes; are they excluded on purpose?

I feel this design gets worse due to its self-imposed linearity.