The only flaw is that the console.log states that null means user is not logged in.

If there are three or more explicit states, you should not use a nullable bool, but some more explicit data structure, like enum.

For example, if the state comes from a db, the user could be successfully logged in, but somehow for a range of possible reasons this variable ends up as null and you'll have a hell of a time debugging, because the log will give you nonsense.