So basically, the problem is that the shifter is set up as a non-standard controller, and games (at least the ones I tried) couldn’t detect it.
To fix this, I used AntiMicroX[https://github.com/AntiMicroX/antimicrox] to remap all the controller inputs to keyboard inputs. I mapped the inputs to the numpad keys (1 to 9).
In the games, you just need to assign the gears to the corresponding numpad numbers, and it should work.
I couldn’t find a solution online for this, so I tried experimenting on my own, and this seems to work for now. I hope it helps! :)
Additionally, to check if your shifter is detected by Linux, you can use tools like evtest or jstest.