Steam input not working for Kingdom Come Deliverance 2

[fxntxsmx]

I am using XBOX Elite Wireless Controller Series 2 to play Kingdom Come: Deliverance 2. I can play fine without Steam Input enabled. When I try enabling Steam Input and map back pedals to other buttons, back pedals don't work. It's as if I'm playing without Steam Input enabled.

Here's how I set up Steam Input for this game:
First, I enabled Steam Input for Xbox controllers and installed Xbox Extended Feature Support Driver in Steam, as shown in the screenshot.
https://ifh.cc/v-Av08Z5

Second, I remapped rear buttons to other buttons as shown in this screenshot. This screenshot also shows that Steam Overlay is enabled.
https://ifh.cc/v-96yybq

But in game, none of the back pedals work as expected: they do nothing.

I tested buttons in Steam Controller Layout and all the buttons work as expected. Here's the video
https://ifh.cc/v-XnGWOg

It seems I can use rear button remaps as expected in the Steam GUI: only in actual game the rear buttons don't work.

How do I fix this?