Support enabling containerd image store

[daniel-amag]

After the update from Docker v23 to Docker v26 the default docker driver currently supports the registry cache backend but only when containerd image store is enabled. The default docker driver is a lot faster than the container driver when you need to use the --load flag.

I've tried enabling this by creating a daemon config file with

{
  "features": {
    "containerd-snapshotter": true
  }
}

and then instructing the daemon to use it upon restart but it doesn't seem to work.
nohup /usr/local/bin/dockerd --host=unix:///var/run/docker.sock --host=tcp://127.0.0.1:2375 --experimental --config-file /etc/docker/daemon.json &

This will always give this error if I try to build with the registry cache backend:

ERROR: Cache export is not supported for the docker driver.
--
282 | Switch to a different driver, or turn on the containerd image store, and try again.
283 | Learn more at https://docs.docker.com/go/build-cache-backends/

[BwL1289]

I am completely blocked by codebuild not utilizing containerd. Large images w/ many layers simply won't work in codebuild without it and will fail either on provisioning stage due to max layers exceeded, or if you're pulling a docker image inside codebuild, will also fail with max layers exceeded.

This is a critical to implement. Squashing images isn't an option for us.

Linking #730 and this #26 (comment)

[BwL1289]

To make matters worse, if you are using cdk pipelines, your entire build flow will not work even if one image with the above error occurs. This needs to be fixed.