You're having a problem with Sunshine. The udev rules work fine, because the controller is officially supported in the kernel. If it's detected, it's working fine.
If it's NOT working with Sunshine involved, that's a Sunshine problem.
Test with the calibration tools of your DE, and also under Steam. If everything works everywhere else, it's not udev which is only responsible for detecting and capturing the device input.
If you think it's a group problem, then...just...add your user to the group maybe?