Which version of Microsoft Edge are you using? And, can you tell us the Windows OS version?
Please check the following configuration to Enable Integrated Windows Authentication:
1. Open Internet Explorer and select "Tools" dropdown.
2. Select the "Advanced" tab.
3. Scroll down to the "Security" section until you see "Enable Integrated Windows Authentication". Select the box next to this field to enable.
4. Select the "Security" tab.
5. Select "Local Intranet" and select the "Custom Level" or "Advanced" button.
6. Scroll down to "User Authentication" > "Logon".
7. Checked the "Automatic logon with current user name and password" option.
8. In the "Security" tab, select "Local Intranet" option and click the "Sites" button.
9. Click the "Advanced" button, then, add your website to the zone.
10. Close the window and apply the configuration.
If still not working, I suggest you could feedback your issue to Microsoft Edge forum, like
this thread.