Hey everyone, I had the same network issues with Ubuntu 22.04 as described above.
The reason for that is a change in the firewall (ufw) as described here: https://www.cloudwizard.nl/lxd-ufw-configuration-ubuntu-22-04/
The solution is to allow lxdbr0 traffic as mentioned on the website:
sudo ufw allow in on lxdbr0
sudo ufw route allow in on lxdbr0
sudo ufw route allow out on lxdbr0
sudo ufw disable && sudo ufw enable
After executing those commands, my VM could finally access the network and also install OS updates.