If you want podman equivalents, you can either use pods of multi containers are the need, or if multi arch builds are the main buildx need, OCI manifests work.

Fedora and selinux may be a thing to look into if you were trying to share volumes.

I am posting this from a park on my phone, so this may be slightly wrong, but this is the multiarch case that seems to be harder to find for many people.

      podman manifest create my-image:latest
      podman build --platform linux/amd64 --manifest my-image:latest .
      podman build --platform linux/arm64 --manifest my-image:latest .
      podman manifest push my-custom-image:latest docker://docker.io/user/my-image:latest

All depends on your needs, but even with docker I prefer moving forward with OCI when possible, preferring standards to product specific workflows.