JWT authentication is stateless by nature and this means that handling user sessions is a bit different than traditional methods of authentication.
On the client side you can use the expiry time of the access token to give a 'hint' that the user is authenticated. Really, that determination comes down to whether or not the access token is valid, but that's a check that can only be made on the backend. You can use the expiry time for the access token to conditionally hide and show various UI elements. You will also put in a method to remove the tokens from local storage so that the user can be considered logged out.