You get the Number type, but not the constructor ( note that you do get the deconstructor ).

No, you are not supposed to use the constructor. Not a kata issue.

I'm not sure I understand the issue here.

Mapping "()" to a leaf, and "(()())" to Leaf :*: Leaf can work, but you still have to deal with all strings, including "". That's the puzzle: you need to figure out a representation that handles every possible string.

If we only kept the parensToTree (treeToParens Tree) test case that would only show that treeToParens is a surjection, not a bijection. You need the other test to show it's a bijection.

I tried using the constructor and ran into this, too.

You don't need the constructor, though.
The kata is solvable with just the provided imports, so I don't think this is an issue.