Detect if authentication is set to “remember” a user being logged on

You can not and probably should not.

The proper full name of that setting should have been “remember me on this browser (for 14 days)”. The point is that it is not even a user based settings and it can have different values on the same computer with different browser sessions.

In addition since it is fully user controlled you should not rely on it to have anything to do with what the user actually sent in the form at login time.

Of course if you have a use case in which the problems mentioned above do not apply, you can just set additional cookie that specifies that the user selected “remember me”

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