Mail still running background activity.

Mail is not running background activity, Mail is responding to Events, meaning arriving email notifications. Any app that receives a notification can run to process that notification. That is not Background App Refresh, which enables an app to run on its own schedule, for example, to reorganize its database, or in the case of Photos, to link photos to the default albums. If you don’t want mail to respond to events you will have to set updates to Manual, and not use Push or Fetch to retrieve email.