If you are still showing log entries, or the states changing on the device page, when you press buttons then the device is still talking to the hub, which means it has not been factory reset or excluded (correctly).
We are getting a lot of conflicting and confusing info, because somewhere else you said nothing was being logged, now you say buttons are being logged.
There is a setting, which is off the bottom of your screenshot, to disable programming from the paddle. If that is turned on the 3x tap on the paddle no longer puts it into exclusion mode. You need to turn that setting off to exclude.
Have you power cycled the device at all, via the breaker, not just the air gap? Sometimes that can help when they get into a bad state.
When you go to exclude, manually start exclusion from the z-wave details page, not from the device page. This is to be sure the hub is really going into exclusion. You may want to have logs open while you run it.
If you still cannot get it to exclude then I would look in the manual for the factory reset procedure and do that. Once it is really reset it will not longer talk to the hub at all. You can verify by testing some actions, nothing should show in logs or the device page. At that point you can try to remove the ghost node: How To Remove Ghosts using hub tools or a UZB Stick
If you can remove the ghost node then great, if not then dont worry about it right now. You can then include the device back to the hub again. It will create a new device in the hubs device list, and a new node in zwave details.
Once that is done you can force remove the old device from the hubs device list to get rid of it, the zwave node may still be stuck there if it being stubborn.
