The Spen options show up everytime I'm charging the phone (Note10+) wirelessly and horizontally, and the spen icon shows up on the notification bar.
When I put S Pen inside, the icon is blinking, probably charging after use. I have Note10 and have Samsung Convertible Fast Wireless Charger(2017 model?). I always put phone vertically, but did test horizontally(on both sides), no traces of S Pen air actions. Try going to settings>advanced features>s pen> on "when s pen is removed" option, pick "do nothing". Try to charge your device as you stated. See if air actions appear