I may have found a fix or workaround for Edge not finding the internal server(s) when launching the public web app at app.plex.tv.
Open Control Panel, Internet Options. Select the Security tab. Click Trusted sites, click Sites button, and add https://app.plex.tv to the list of websites. Close all of the Internet Properties windows.
Close any open Edge windows. Open a new Edge window and open app.plex.tv. It should now find your default server. If you open the server list and select any of your other servers (if you have more than one) they may show as not found, but if you click on said server name it will connect.