Is there a REST endpoint for getting the logout token? So I know the logout_token is generated along with the csfr_token during the POST to /user/login?_format=json.

You can get a copy of the csfr_token for the session at any time by calling a GET on /session/token. Is there a way to get the logout token outside of the user logging in? So is there a path that once logged in will provide you with the logout_token? I'm looking for a way to clear a cookie that gets stored beyond the initial session.
It appears this does not currently exist. I just created a patch for core. Please review it and make suggestions if you have a chance. https://www.drupal.org/project/drupal/issues/3004421

I will edit this answer if any progress is made with the patch.