Debian often send you local mail for updates or stuff like this, because I find it really annoying, if I get mail notification in my shell. This is stuff from the 80s and no longer needed on mordern system.
To disable the local mails I just set a blackhole alias for my user to drop all this mails. I used this with the default debian exim config. Here is my /etc/aliases
# /etc/aliases mailer-daemon: postmaster postmaster: root nobody: root hostmaster: root usenet: root news: root webmaster: root www: root ftp: root abuse: root noc: root security: root root: dgo dgo: :blackhole:
You just have to add the :backhole: behind your user. The exim will drop all mails.