Can I access the AuthenticateResult.Fail exception parameter in other middleware?

In my AuthenticationHandler I have some (shared) code like:

 try
    {
       doSomething()
    }
    catch(AuthException e)
    {
        return AuthenticateResult.Fail(e);
    }

I would like to be able to access that exception in other middleware. something like :

public async Task Invoke(HttpContext context)
{
 context.   ??? AuthenticationContext.Exception?
}  

I know this is somewhat old question, but to solve this, I decided to use HttpContext.Items in my implementation of IAuthenticationService to put a value with key like AuthenticationException there, and then read that in other middleware or filter.

Note that It may look tempting to use HttpContext.Features.Get<IAuthenticateResultFeature>().AuthenticateResult, but this feature is not set for failed authentications! I've spent several hours debugging this, only to understand that I need to look for another way.