Good to know Proxmox’s bad updates are more pervasive than the latest bad update.
I have been able to install Docker in the LXC containers and pull images in with the normal commands. I do that container-in-container to get effectively rootless docker containers for stuff that I couldn’t figure out how to run rootless. So you don’t even lose out on docker if you’re determined! And as you said incus goes on any OS, you can docker just fine on the base OS of your choice and use incus for specific things!
In incus, I had the same setup of an LCX container with a Docker container inside of it. I passed 1000/1000 to the LXC container but the LXC container’s default root user has a an ID set of 0/0. So I had to pass 0/0 to the Docker container, not 1000/1000 to get the read/write permissions working.
That may fix your issue as it’s basically the same tech, just different automated things implementing the LXC container!