`TH.reifyType` reports `StarT` instead of the actual kind synonym

Summary

When applied to a name of a type synonym, Language.Haskell.TH.reifyType seems to always return Type even if the intent is to define a kind definition.

Steps to reproduce

Note that the TypeConstructor is treated as a synonym of kind Type -> Type throughout the following short program. However the TH splice prints StarT as its kind.

{-# Language KindSignatures, TemplateHaskell #-}

import Data.Kind (Type)

import Control.Monad.IO.Class (liftIO)
import qualified Language.Haskell.TH as TH

type TypeConstructor = Type -> Type

type Identity :: TypeConstructor
newtype Identity a = Identity {runIdentity :: a}

main = putStrLn (runIdentity $ Identity "Hello, World!")

$(TH.reifyType ''TypeConstructor >>= liftIO . print >> pure [])

The KindSignatures extension is irrelevant, I've only added it to illustrate that everything works outside of TH. The output of the program is

$ runhaskell BugDemo.hs
StarT
Hello, World!

Expected behavior

$ runhaskell BugDemo.hs
AppT (AppT ArrowT StarT) StarT
Hello, World!

Environment

• GHC version used: 9.6.2

Optional:

• Operating System: Fedora Linux
• System Architecture: x86_64