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I think what you need is a local registry mirror on the rancher desktop instance.

limactl shell <instance>
    sudo -i
    cat <<EOF > /etc/rancher/k3s/registries.yaml
    mirrors:
      localhost:
        endpoint:
          - "<http://localhost:5000>"
    EOF

I use dockerd, so can't speak on nerdctl. I created a ~/Docker-Storage directory to contain pushed images.

docker run -d --restart=always -p "127.0.0.1:5001:5000"

-v ~/Docker-Storage:/var/lib/registry --name registry registry

Then for images to be accessible, you tag to localhost:5001 and push there. But, image locations in charts or variable files will need to point to this localhost:5001.

The pull was resolved by adding --namespace k8s.io to the nerdctl build https://rancher-users.slack.com/archives/C0200L1N1MM/p1680534667981599