Math Easy Solutions, that’s usually a pen hardware issue, not OneNote being haunted: the Surface Pen can start “inking while hovering” if the tip switch is stuck, the nib is worn/misaligned, debris is jammed around the tip, or a screen protector is interfering with hover detection, which multiple Surface users report and Microsoft’s own support threads describe (Microsoft Answers, Surface Reddit thread).
The fastest fixes are: pull out and reseat/replace the nib, remove any screen protector to test, restart the device, and re-pair/update the pen and touch drivers; if it still writes before contact, the pen tip sensor is probably failing (Microsoft Answers, Surface Forums).
I don’t see a relevant InLeo thread from you on this, so I’d bet on the pen itself before blaming OneNote.