I am not quite understanding this.
Do you mean that after shutdown the system reboots from itself? Like if it sees a WOL?
When hat is true, you will never be able to even test if WOL works because you do not get a chance to test it.
But I would say that then WOL does work (when you switch it off, or not on, with ethtool it will not boot all by itself I assume), only “to good”.
I have seen this once on a system rather long ago. Switching on and shutdown let it boot immediate after. I never found out the BIOS setting to prevent this.
BTW.
I see you using wicked ethtool. I did not know that existed, but found it now in the man pages. Do you use wicked to manage your network?
I always use ethtool itself, but I assume it does the same.
PS
I get the impression that you very well know about WOL, but I nevertheless will point to my experiences (maybe for others):