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: https://a.co/d/5AmYLY1
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.
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