I am sorry that your replies that are marked as answer will not solve this issue for anyone.
this is me writing you from Edge via Mobile Hotspot, because Edge on Windows 1809 does not work at all if the network is configured to private or Domain on the very same device.
This shows that the issue is not necessarily a thing that a user has in his hands, especially not in Enterprises.
BE AWARE THIS ISSUE WAS NOT PRESENT IN RS5 17713
Situation in RS5 17763.1 (GA)
Error when trying to load ANY site:

There are many threads that discuss the same issue, while I consider this to be the main thread, as long it does not get locked up as some of the others - without reference to this one.
**Some even report a coincidence with Sophos XG,**and Sophos is pointing to Microsoft Driver Changes in 1809 here.
https://community.sophos.com/products/endpoint-security-control/f/sophos-endpoint-software/105637/edge-browser-being-blocked-after-windows-10-update-1809?pi2147=5
https://community.sophos.com/kb/en-us/132874
The CU 10-2018 for 1809 does not fix the issue.
Be aware that Microsoft "Solutions" that includes resetting Edge (incl. loosing history), activating IPv6 or Setting up the Internet connected Network Adapter to Public Network do help but cannot be advised in Enterprises.
reference:
https://answers.microsoft.com/en-us/windows/forum/windows\_10-start/microsoft-edge-not-working-cant-browse-to-any/32893f86-7a4d-4eec-9eb3-eb683705a71e
The network adapter is naturally set to Domain Network for Domain Joined Computers and should / cannot be changed. Also for sake of working (Advanced) Windows Firewall Settings.