Just wanted to chime in with my findings:
I'm using an Xbox One Gamepad, connected by Bluetooth to my Mac running Monterey (12.0.1). When just using MacOS, the bluetooth connection works well - pairs quickly and stays connected. Works great with (Mac) Steam games.
In Parallels, when I select "Share Bluetooth devices with Windows" in the settings, I can successfully pair the controller over bluetooth with my Windows 11 ARM VM. It takes a bit longer, but eventually gets connected. However, the controller never shows up in "Game Controllers", and no Windows games recognise the controller.
If I use a wired connection via USB and allow it to connect to the VM instead of my Mac, it shows up as expected and works great.
This is with Parallels 17.1.1 running on my M1 MacBook Air. I can use a wired connection for now, but I would really like bluetooth to work in the future.