I don't know much about Edge, but to me it looks like some kind of DNS problem. Could it be that Edge is using some kind of proxy/filter and thus does not use the same DNS servers as the other browsers?
(I know that when using Firefox though a proxy there is a setting for using DNS though the proxy or through the local machine. I know this just because I have been using Firefox through a putty-tunnel to access my LAN at home, when I wanted to be able to use the local LAN machine names I had to change that setting.)