This sounds like the same kind of issue you would see with joystick drift. Please see my answer below for that repair.
Drift is a common problem with all joysticks. The best way to solve that problem with with a joystick replacement. The Hori Split Pro appears to be compatible with Xbox joystick replacements like can be found anywhere you search for "xbox joystick replacement". For example: [link|https://a.co/d/5AmYLY1?tag=ifixitam-20|https://a.co/d/5AmYLY1|new_window=true]
The existing joystick would need to be removed/unsoldered and replaced with a new joystick. This is a common repair for any controller with a joystick. Search YouTube for thousands of videos on how to do it.