Error GHC-91510: illegal polymorphic type

Mmm, indeed—the change to type Objects c :: k -> Constraint seems to be necessary for GHC 9.14 to handle the quantified constraint, though I don’t really know why.

Unrelatedly, you lost the precondition on type Objects (Transform c d); CCompose (Objects d) is too strong. Call me crazy, but how about:

class (Category c, Category d, Objects c ==> ObjectClass d . f)
   => Functor c d f where
  map :: a `c` b -> f a `d` f b

instance Category (Transform c d) where
  type Objects (Transform c d) = Functor c d
  ...