Question regarding/about the XBOX Game-pad Extension

XBOX gamepad ext only supports Xinput / DirectInput controllers (Xbox controllers) so it won't support others like DualShock 4 or Switch controllers unless they are running as Xinput controllers (achieved by using an app like DS4windows) or mapped as such from steam controller input settings

So to natively support other controllers, you would want to use other extensions..
Unfortunately Joystick2 is a very old ext, with many problems, and it needs many workarounds to work as intended (also it's generally missing some modern features, and doesn't support other runtimes)
Volnaiskra already made a workaround engine for that called Vaccine, but in general you don't even need to go with Joystick ext anymore, unless maybe your game already heavily relies on it..

A much better option would be to go SDL, there are two variations:

• The original PKR made one (SDL Joystick), it's free, but doesn't have the same amount of features as te paid version made by Phi, also it's a bit harder to use, though still a decent option to go with, much better than going with something like Joystick2 (it's free and open-source after all): Please login to see this link.
• An Upgraded one made by Phi, it's paid, but has more features like support for other runtimes, and things like Gyro, touchpad and LED support, also it's easier to use and better documented in general, this is the version I would go with if i'm willing to pay a few bucks (the real value of that can differ from country to country ofc)
  I think you may need to contact Phi and/or join his patreon to get it (I personally got it along other extensions after joining his patreon for few months, then contacting him about it via discord, but I think you can get it without joining his patreon by paying it's price separately)

Go with whatever SDL version suitable for you, but in general try to avoid Joystick2 and Xbox gamepad unless absolutely necessary.