How to write a Haskell program that initiates and can then run commands in a nix-shell environment?

Question

I would like to initiate a nix-shell (if unfamiliar with Nix), this can be thought of as a bashs hell that loads a particular environment, somewhat expensively). Once initiated as a separate process, I'd like to be able to send commands to that shell and retrieve the results. There is the potential for some complexity here related to concurrency issues, but I thought shelly might be able to simply handle it like this:

#!/usr/bin/env stack
{- stack script --nix --resolver lts-14.27
     --package async
     --package shelly
-}

{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ExtendedDefaultRules #-}
{-# OPTIONS_GHC -fno-warn-type-defaults #-}
  
import Shelly

main :: IO ()
main = shelly $ do
  run_ "nix-shell" ["-p", "cargo"]
  run_ "cargo" []

In the first run_, we initiate a shell that has the cargo command available, which we should then be able to run using the second call to run_. However, this results in an error where the PATH does not seem to be correct - strangely it no longer containers even nix-shell in the path.

I'd be open to suggestions on how to do this using various approaches, not necessarily with shelly.