Mock IOptionsMonitor

You are calling the constructor of the OptionsMonitor<TOptions> class incorrectly.

In this case I would have just mocked the IOptionsMonitor<AuthenticationSettings> interface

For example using Moq

AuthenticationSettings au = new AuthenticationSettings() { ... };
var monitor = Mock.Of<IOptionsMonitor<AuthenticationSettings>>(_ => _.CurrentValue == au);
ActiveDirectoryLogic _SUT = new ActiveDirectoryLogic(monitor);

Achieving the same in NSubstitute:

        var optionsMonitorMock = Substitute.For<IOptionsMonitor<AuthenticationSettings>>();
        optionsMonitorMock.CurrentValue.Returns(new AuthenticationSettings
        {
            // values go here
        });

Here is another way to do it that doesn't involve trying to set the readonly CurrentValue field.

using Moq;

private IOptionsMonitor<AppConfig> GetOptionsMonitor(AppConfig appConfig)
{
  var optionsMonitorMock = new Mock<IOptionsMonitor<AppConfig>>();
  optionsMonitorMock.Setup(o => o.CurrentValue).Returns(appConfig);
  return optionsMonitorMock.Object;
}