First of all, let’s check if you're encountering the same issue I did.
Open Steam, go to the top-left corner and click Steam > Settings > Controller, then see if any additional devices are being detected.
In my case, it shows both "XBOX SERIES X CONTROLLER" and "KEYCHRON LINK" (which is my keyboard).
Even after disabling all the options under the keyboard, I still couldn't get the controller to work in-game.

To fix this, open Device Manager, go to the Human Interface Devices section, and disable the HID-compliant game controller.
After doing this, your controller should work properly.

My assumption is that Steam Input, or some games, use HID to make input devices compatible with the game.
Steam might mistakenly detect keyboards that support customization, like macros or key remapping as a game controller.
When the keyboard is recognized as Controller 1, your actual controller gets pushed to Controller 2, and the game will ignore its input settings.

I’m not sure if there’s another way to change controller priority, but this workaround has worked for me for now.