DO NOT migrate / upgrade anything to the snap package
It was already in place when I came in (made me roll my eyes), and it's a mess. As you said, there's no proper upgrade path to anything else. So anyway...
you should migrate into LXD LTS from Debian 12 repositories
The LXD version in Debian 12 is buggy as fuck, this patch has not even been backported https://github.com/canonical/lxd/issues/11902 and 5.0.2-5 is still affected. It was a dealbreaker in my previous tests, and doesn't inspire confidence in the bug testing and patching process on this particular package. On top of it, It will be hard to convice other guys that we should ditch Ubuntu and their shenanigans, and that we should migrate to good old Debian (especially if the lxd package is in such a state). Some parts of the job are cool, but I'm starting to see there's strong resistance to change, so as I said, path of least resistance.
Do you have any links/info about the way in which Proxmox kernels/packages differ from Debian stable?