Is there a way to detect a user logged into Microsoft Edge via c# code

One of our clients have staff members authenticated via SSO in Microsoft Edge using Entra - https://learn.microsoft.com/en-us/deployedge/microsoft-edge-security-identity - Does anyone happen to know if there is a way of being able to detect the user that is logged into Microsoft Edge via c# code? The screenshot below shows what I mean when I say a user is logged into Microsoft Edge.

I have looked at the httpcontext and the cookies, but cannot see anything that would help me detect the user that is logged into Microsoft Edge.

If this is not possible, that is also fine, but would be good to know one way or another so any help would be appreciated.