Types of Typed Spliced are not inferred (looks like only checked)

I think this might be duplicate of #10271, but I'm not sure. This example is simpler.

Consider a small utility type-class (a variant discussed in !3290 (closed)

{-# LANGUAGE GADTs #-}
module CodeFromString where

import           Language.Haskell.TH
import           Language.Haskell.TH.Syntax

class CodeFromString a where
    codeFromString :: String -> TExpQ a

instance a ~ Char => CodeFromString [a] where
    codeFromString = liftTyped

It seems to work

{-# LANGUAGE TemplateHaskell #-}
module Main (main) where

import CodeFromString

main :: IO ()
main = do
    putStrLn $$(codeFromString "example string")

Yet, if we make the setting just slightly more complicated like:

    -- doesn't work
    print $  $$(codeFromString "example string") == "example string"

    -- doesn't work
    print $  $$(codeFromString "example string") == ("example string" :: String)

The type of splice TExpQ String should be easily inferrable, but GHC refuses to infer it. If we make GHC check the type with

    -- works.
    print $  ($$(codeFromString "example string") :: String) == ("example string" :: String)

it works again. But the explicit type-annotation / checked positions make this kind of usage quite impractical.

cc @mpickering