You can set up automatic reboot after Unattended Upgrades has upgraded/installed something that requires reboot. That includes installing new kernels.

Related configuration variables:

// Automatically reboot *WITHOUT CONFIRMATION* if

//  the file /var/run/reboot-required is found after the upgrade

//Unattended-Upgrade::Automatic-Reboot "false";



// Automatically reboot even if there are users currently logged in

// when Unattended-Upgrade::Automatic-Reboot is set to true

//Unattended-Upgrade::Automatic-Reboot-WithUsers "true";



// If automatic reboot is enabled and needed, reboot at the specific

// time instead of immediately

//  Default: "now"

//Unattended-Upgrade::Automatic-Reboot-Time "02:00";

Save your preferred settings in file /etc/apt/apt.conf.d/52unattended-upgrades-local (so that you do not have to modify 50unattended-upgrades provided by the package).

You can see explicitly set configuration values by
apt-config dump unattended-upgrade

Unfortunately, you can not list all current values.
https://github.com/mvo5/unattended-upgrades/issues/245

You could see more documentation (of the latest version) at https://github.com/mvo5/unattended-upgrades

Unfortunately not all supported options are explained there, though:
https://github.com/mvo5/unattended-upgrades/issues/246
https://github.com/mvo5/unattended-upgrades/issues/318