workflows/docker: use docker/build-push-action to build images

[ZhongRuoyu]

• Have you followed the guidelines in our Contributing document?
• Have you checked to ensure there aren't other open Pull Requests for the same change?
• Have you added an explanation of what your changes do and why you'd like us to include them?
• Have you written new tests for your changes? Here's an example.
• Have you successfully run brew style with your changes locally?
• Have you successfully run brew typecheck with your changes locally?
• Have you successfully run brew tests with your changes locally?

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This allows us to use Docker's build cache across workflow runs.

Follow-up to #18168 (comment).

[ZhongRuoyu]

docker/build-push-action needs to be whitelisted: https://github.com/Homebrew/brew/actions/runs/10571630424

[MikeMcQuaid]

docker/build-push-action needs to be whitelisted: Homebrew/brew/actions/runs/10571630424

Done! Do we want/need to use https://github.com/docker/setup-buildx-action or https://github.com/docker/login-action?

[MikeMcQuaid]

Looking good so far, thanks @ZhongRuoyu!

[carlocab]

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

[ZhongRuoyu]

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

We probably need Docker Buildx for this: https://github.com/docker/setup-buildx-action. @MikeMcQuaid will you whitelist this too?

[MikeMcQuaid]

We probably need Docker Buildx for this: docker/setup-buildx-action. @MikeMcQuaid will you whitelist this too?

Done!

[MikeMcQuaid]

Thanks @ZhongRuoyu!