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This isn’t possible on the server side and beyond nginx control. The nature of SSL is that it can authenticate and authorize, but it will use a session to remember it’s decisions.
Think of the site as a building. Once you are authenticated using some kind of keycard you are let in and you can freely walk around. There may be areas that you need additional authorization for and your credentials provided at the entrance will be used for that.
What you are asking for is that when you drop your keycard you will be picked up instantly and removed from the building.
You see the issues with that and the normal procedure is to walk out of the building, meaning a client side action. Your best bet is thus to send a logout request from the client side once the keycard is removed. This is a topic in it’s own right as answered here.