docker:dind does not match DOCKER_VERSION anymore

Checks

• I've already read https://github.com/actions/actions-runner-controller/blob/master/TROUBLESHOOTING.md and I'm sure my issue is not covered in the troubleshooting guide.
• I'm not using a custom entrypoint in my runner image

Controller Version

v0.27.0

Helm Chart Version

0.22.0

CertManager Version

No response

Deployment Method

Helm

cert-manager installation

certmanager works

Checks

• This isn't a question or user support case (For Q&A and community support, go to Discussions. It might also be a good idea to contract with any of contributors and maintainers if your business is so critical and therefore you need priority support
• I've read releasenotes before submitting this issue and I'm sure it's not due to any recently-introduced backward-incompatible changes
• My actions-runner-controller version (v0.x.y) does support the feature
• I've already upgraded ARC (including the CRDs, see charts/actions-runner-controller/docs/UPGRADING.md for details) to the latest and it didn't fix the issue
• I've migrated to the workflow job webhook event (if you using webhook driven scaling)

Resource Definitions

does not apply

To Reproduce

1. Install the Helm Chart with default values for `images:`
2. Use buildx with inline cache

Describe the bug

On February 4th the official docker:dind tag got updated to 23.0.0.
The DOCKER_VERSION used in the runner-image is pinned to 20.10.21
So when using the default values of the Helm Chart the docker client and server versions don't match.

For me this led to a problem using the [docker/build-push-action](https://github.com/docker/build-push-action with an inline cache configuration:

Error: buildx failed with: ERROR: failed to receive status: rpc error: code = Unavailable desc = error reading from server: EOF

Pinning the sidecar image to docker:20.10-dind fixed the issue for me.

Describe the expected behavior

Maybe the default image tag in the Helm Chart should be tied to the DOCKER_VERSION specified in the runner Dockerfiles.

Whole Controller Logs

https://gist.github.com/norman-zon/0e1de4e82cd937c979457d988ad20ad7

Whole Runner Pod Logs

don't have the runner logs anymore

Additional Context

No response

Start with the Helm chart's default image values and runner/actions-runner.ubuntu-22.04.dockerfile, where DOCKER_VERSION is pinned. Reproduce the mismatch with buildx and inline cache, then verify that the default sidecar image and runner Dockerfile use compatible Docker versions and the reported error no longer occurs.