Use role-based authentication to push images

[sikachu]

This PR updates all workflows in this projects to use role-based authentication instead of access key pair to authenticate with public ECR repository.

We want to move to role-based authentication as it's more secured than using access key pair. The previous access key pair has been revoked.

Because this is a public repository, the PUBLIC_ECR_ROLE and AWS_REGION has been set via repository secrets.

I've confirmed that this is working:

• build-rails-base: https://github.com/komoju/dockerfiles/actions/runs/26437972031
• build-rails-buildpack: https://github.com/komoju/dockerfiles/actions/runs/26437971991
• clone-images: https://github.com/komoju/dockerfiles/actions/runs/26437972030

Note that this PR also modernize the way we build and push image by using actions instead of calling docker directly.

[harsh-gulhane]

LGTM!
Thank you for fixing.

Just noticed that this repo was missed during the self-hosted runner migration; I will raise a separate PR. Not required as it's a public repo.