That sounds familiar. Bluetooth connection causing stutter happened before in a number of ports.
I've fixed issues like this before.
I feel like when it comes to controller support a lot of Japanese developers try to do
too much (and then run into failure states / corner cases / bad behaviour). Especially in a single-player game released on Steam, just
don't bother implementing anything other than Xinput (or Steam input if you only target Steam). That's basically
completely stateless, and your game won't mess up or stutter or anything regardless of what happens to your player's controllers. And Steam will allow them to use any controller they realistically want seamlessly with 0 lines of code (that can go wrong) on your part.
When you start integrating e.g. 4 different controller APIs, and scan all USB devices for their IDs to do some smart mapping, the chance of something going wrong is infinitely higher for basically no practical gain.
FWIW, to me none of the Nier stuff sounds dealbreaking. 60 FPS sucks, but I can't say I expected more from S-E.