Log out from Google account on Android 6.0.1
Partly answering my own questions:

It appears that you can sign out any (other) device by going to Google's recently used devices list and revoking the device's access. At the very minimum, the Play Store app will whinge with a permanent notification (one of the kind that won't go away, no matter how many times you acknowledge it) that you need to sign in again.

Edit: The notification goes away if turn off notifications for Play Store and turn them back on.

The downside: 

Under syncing of app data etc. still happens under Settings -> Cloud and Accounts -> Accounts -> Google if triggered manually. Not sure how that's possible if the device has access revoked...

Man alive, this is an awful user experience... If Google was asking money for this kind of service, they'd be bankrupt tomorrow.