The issue causing the failure is that the test class cannot be a MonoBehavior, as it the test class is constructed, but not instantiated. An alternative solution to this is to just yield the method that needs to run as a corutine, then the test runner picks it up and runs it.

public class CoroutineTest2
{

[UnityTest]
public IEnumerator CoroutineTry()
{
Debug.Log("Starting Coroutine Test!");
yield return TestTwo();
Debug.Log("This message should be shown last");
}

IEnumerator TestTwo()
{
yield return null;
Debug.Log("Running in coroutine");
yield return null;
}
}

An alternative solution is to split the mono behavior away from the test, create a new game object and then add the mono behavior to that. E.g.
public class CoroutineTest
{

[UnityTest]
public IEnumerator CoroutineTry()
{
Debug.Log("Starting Coroutine Test!");
var go = new GameObject();
var mb = go.AddComponent<MonoBehaviorWithCorutine>();
mb.RunAsCorutine();
yield return null;
Debug.Log("This message should be shown last");
}
}

public class MonoBehaviorWithCorutine : MonoBehaviour
{
public void RunAsCorutine()
{
StartCoroutine(TestTwo());
}

IEnumerator TestTwo()
{
yield return null;
Debug.Log("Running in coroutine");
yield return null;
}
}