I do not know whether the LXD snap package adds some extra level of indirection.
I suggest to try with Incus and document the steps you take (I mean, post them here).
Show the steps like this person here, GPU in a docker instance
What you are facing is not that the GPU is not accessible from Docker in a container, but rather that the specific NVidia Docker application container has certain, perhaps unrelated, requirements that are not met. Hence, this specific NVidia Docker application container does not start.
I had a similar issue when I was trying to run Telegram in a GUI container. The application wanted access to the console, otherwise it would crash.
So the weird thing here is that NVIDIA contributed both the LXC and Docker integrations.
But they made it so that the LXC integration only works with unprivileged containers whereas the Docker integration only works with privileged containers, so that’s how we end up with this weird mess.
The only workaround I’m aware of is to not use nvidia.runtime on the Incus side but instead go through the annoying process of installing all the NVIDIA packages directly in the Incus container, at which point, that container can be privileged and the Docker support should work as expected.