If the LXD snap isn’t installed already on the new system then running sudo snap install lxd will put you on the stable release channel rather than the long term support (LTS) 4.0 channel.
So if you’re looking to have a more modern system but still follow a similar release cadence as 3.0 LTS branch then I would recommend you switch to the 4.0 LTS channel using:
sudo snap install lxd --channel=4.0/stable
sudo lxd.migrate
I am not sure of the specifics of the lxd.migrate command but my understand is that it updates the database and some file locations, but largely leaves your containers untouched. But as ever, certainly worth having a fresh backup before attempting any major upgrade.