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.