Hello -
How do you determine online/offline state of your computer? I have a solution that uses PING to report status back to an Edge driver. It requires a couple Python scripts to be running on a separate, always-on computer.
I have two drivers that include the WOL function - my LAN device monitor (which it sounds like you tried), and a standalone WOL driver and works with Alexa.
You probably cannot use this driver to monitor your online/offline status (it is for UPnP devices), but it definitely should work fine for sending WOL command to your computer. You just need to be sure you have the mac address entered correctly.
My Web Requestor driver could probably be used to do this.