Ok, found the answer myself:
root@photoview:~# dmesg | grep overl
[270044.387623] overlayfs: idmapped layers are currently not supported
[270046.650667] overlayfs: idmapped layers are currently not supported
[270048.896203] overlayfs: idmapped layers are currently not supported
[270242.494895] overlayfs: idmapped layers are currently not supported
[270244.647997] overlayfs: idmapped layers are currently not supported
[270246.901194] overlayfs: idmapped layers are currently not supported
root@photoview:~# mount | grep idmap
/dev/sda4 on / type btrfs (rw,relatime,idmapped,
So maybe sometime in the future, but docker on lxd has quite a few gotchas. Maybe it would work if the host were running 22.04 and its newer kernel? This comment sounds as if it’s a solved issue by now.