Edit: /etc/apt/apt.conf.d/10periodic and append the following:

APT::Periodic::Unattended-Upgrade "1";

This depends on the apt package unattended-upgrades being installed and the log output will be in /var/log/unattended-upgrades

My full 10periodic file looks like:

APT::Periodic::Update-Package-Lists "1";
APT::Periodic::Download-Upgradeable-Packages "0";
APT::Periodic::AutocleanInterval "0";
APT::Periodic::Unattended-Upgrade "1";

This is run by /etc/cron.daily/apt-compat and the full list of configuration options are in /usr/lib/apt/apt.systemd.daily:

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