Is there a single word for “login/logout”? [closed]

Logging in is authenticating and logging out is deauthenticating (or, sometimes, unauthenticating). Code that does both handles authentication.

An example of authentication being used as a hypernym like this can be found in the CakePHP docs:

Authentication (login and logout)

We’re now ready to add our authentication layer. In CakePHP this is handled by the AuthComponent, a class responsible for requiring login for certain actions, handling user sign-in and sign-out, and also authorizing logged in users to the actions they are allowed to reach.

Similarly, the Laravel (another PHP framework) documentation page titled Authentication also covers both logging in and logging out.