internalMutability :: 
  (HasGen env g, MonadReader env m, MonadRandom g m, PrimMonad m) => m Word
internalMutability = do
  w1  <- uniformEnvM
  ref <- newMutVar w1
  w2  <- uniformEnvM
  modifyMutVar' ref (+w2)
  readMutVar ref


data App = App
  { appGen :: MutGen RealWorld StdGen
  , appDbConnection :: () -- hypothetical
  }

instance HasGen App (MutGen RealWorld StdGen) where
  getGen = appGen


runApp :: App -> ReaderT App m a -> m a
runApp app action = runReaderT action app

data AppPure = AppPure
  { appPureGen :: PureGen StdGen
  , appPureDbConnection :: () -- hypothetical
  }

instance HasGen AppPure (PureGen StdGen) where
  getGen = appPureGen

runAppPure :: AppPure -> ReaderT AppPure m a -> m a
runAppPure app action = runReaderT action app

main :: IO ()
main = do
  let g = mkStdGen 217

  gen <- thawGen $ MutGen g
  runApp (App gen ()) $ do
    v <- internalMutability
    liftIO $ print v
  runReaderT (internalMutability >>= liftIO . print) gen

  runGenStateT_ g $ \pg -> runAppPure (AppPure pg ()) $ do
    v1 <- internalMutability
    liftIO $ print v1
    v2 <- internalMutability
    liftIO $ print v2

  let (v1, v2) =
        runST $ runGenStateT_ g $ \pg -> runAppPure (AppPure pg ()) $ do
          v1' <- internalMutability
          v2' <- internalMutability
          pure (v1', v2')
  print v1 >> print v2

λ> main
13567046000262619
2533773515975174092
13567046000262619
2533773515975174092
13567046000262619
2533773515975174092