I finally located the piece I was missing.

The Realm Settings has a variable called SSE Session Idle. This is what implements the desired behavior and expires the token if the user is inactive for a period exceeding the SSE Session Idle.

The Cookie.ExpireTimeSpan just indicates how long till the Cookie is deleted, but as long as the user is within the SSE Session Idle time and no MaxAge has been set on the OpenIdConnect the user can request a new Cookie by making an HTTP request. This also resets the SSE Session Idle timer.