TemplateHaskell typechecking regression in HEAD

(Originally observed in a head.hackage CI job here.)

The what4-1.4 Hackage library currently fails to build with GHC HEAD + head.hackage. Here is a minimized example of the issue:

{-# LANGUAGE RankNTypes #-}
{-# LANGUAGE TemplateHaskell #-}
module Bug where

good :: (forall a. a -> a) -> b -> b
good = \g x -> g x

bad :: (forall a. a -> a) -> b -> b
bad = $([| \g x -> g x |])

This compiles with GHC 9.8 and earlier, but fails to typecheck with GHC HEAD at commit b938950d:

$ ghc-head Bug.hs
[1 of 1] Compiling Bug              ( Bug.hs, Bug.o )

Bug.hs:9:8: error: [GHC-83865]
    • Couldn't match type: b -> b
                     with: forall a. a -> a
      Expected: (forall a. a -> a) -> b -> b
        Actual: (b -> b) -> b -> b
    • In the expression: \ g_a24j x_a24k -> g_a24j x_a24k
      In an equation for ‘bad’: bad = (\ g_a24j x_a24k -> g_a24j x_a24k)
    • Relevant bindings include
        bad :: (forall a. a -> a) -> b -> b (bound at Bug.hs:9:1)
  |
9 | bad = $([| \g x -> g x |])
  |        ^^^^^^^^^^^^^^^^^^^

I think both of these should be accepted, as the only difference between good and bad is the presence of a Template Haskell splice.

While I haven't had time to bisect the issue just yet, my first hunch is to suspect commit !10911 (closed) (Look through TH splices in splitHsApps).