Step 1 - Install the Armbian PGP key and update your APT sources
Install armbian.gpg to /usr/share/keyrings/armbian.gpg (mode 644)
You can use a copy from another one of your SBCs, or...
... you can download and install like below (thanks @BrewNinja for the example)
touch /usr/share/keyrings/armbian.gpg
chmod 644 /usr/share/keyrings/armbian.gpg
wget https://apt.armbian.com/armbian.key -O - | gpg --dearmor >/usr/share/keyrings/armbian.gpg
Edit /etc/apt/sources.list
Replace all instances of bullseye with bookworm
Edit /etc/apt/sources.list.d/armbian.list
deb [signed-by=/usr/share/keyrings/armbian.gpg] http://apt.armbian.com bookworm main bookworm-utils bookworm-desktop
Edit any other files in /etc/apt/sources.list.d as appropriate, to replace bullseye with bookworm
Step 2
apt update
Step 3
NOTE - WHEN RUNNING THE BELOW COMMANDS, DO NOT ACCEPT ANY INTERACTIVE PROMPTS FOR CHANGING /etc/initramfs-tools/initramfs.conf
The default is not to accept the changes anyway - but I am noting this here to be extra careful
I've checked - the changes may differ from what armbian has in the latest images
apt upgrade --no-new-pkgs
apt full-upgrade
apt dist-upgrade