RP2040-PiZero as HID Remapper?

Will the RP2040-PiZero work as HID Remapper?

Yes, we have a build for that board, just keep in mind that it has unnecessary pullup resistors on the USB lines so you may run into some issues where devices don’t work when hotplugged (or only work when hotplugged or something).

What about waveshare RP2350 USB?

Yes, we have a build for that board too with similar caveats.

I got waveshare RP2350 USB. How do I have it act as XBox controller? Input is steering wheel/pedal set. Output is XBox controller. Wheel to left thumbstick X, Brake to left trigger. Throttle to right trigger.

It cannot currently act as an Xbox controller, it can do Stadia and Switch controller, which may or may not work for you depending on the game.