GH-48824: [CI] Fix homebrew-cpp with Mac by using formula-based dependency resolution

[HyukjinKwon]

Rationale for this change

homebrew-cpp with MacOS was failing with No such file or directory @ rb_sysopen errors when downloading bottles for dependencies (icu4c, boost, etc.).

This appears to be caused by Homebrew's JSON API (ghcr.io) returning stale or corrupted metadata on GitHub Actions runners.

Disclaimer: I can't tell what is the actual cause. Seems to be a bug in Homebrew introduced from the latest MacOS runner image but I don't have any evidence for it. What I can see was that there was an recent update in MacOS images with Homebrew upgraded together:

• https://github.com/actions/runner-images/releases/tag/macos-14%2F20260105.0099
• https://github.com/actions/runner-images/releases/tag/macos-15-arm64%2F20260105.0094
• https://github.com/Homebrew/brew/releases/tag/5.0.8

which I believe are related.

What changes are included in this PR?

Add HOMEBREW_NO_INSTALL_FROM_API=1 to the Homebrew test workflow to use traditional formula-based dependency resolution instead of the JSON API.

Are these changes tested?

Tested in https://github.com/ursacomputing/crossbow/actions/runs/20907195327/job/60062808357

Are there any user-facing changes?

No, CI-only.

• GitHub Issue: GH-48824: [CI] Fix homebrew-cpp with Mac by using formula-based dependency resolution #48824

[github-actions]

Thanks for opening a pull request!

If this is not a minor PR. Could you open an issue for this pull request on GitHub? https://github.com/apache/arrow/issues/new/choose

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Then could you also rename the pull request title in the following format?

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See also:

• Other pull requests
• Contribution Guidelines - Contributing Overview

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: 4a9face

Submitted crossbow builds: ursacomputing/crossbow @ actions-892981fcf9

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: 76066f0

Submitted crossbow builds: ursacomputing/crossbow @ actions-8cbd3f47d3

Task	Status
homebrew-cpp

[github-actions]

Revision: 76066f0

Submitted crossbow builds: ursacomputing/crossbow @ actions-4874464f58

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: 4a4410a

Submitted crossbow builds: ursacomputing/crossbow @ actions-b659d645d6

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: e58b8cb

Submitted crossbow builds: ursacomputing/crossbow @ actions-8567fefd86

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: 79a0e5c

Submitted crossbow builds: ursacomputing/crossbow @ actions-49e935cfaf

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: cdeadc2

Submitted crossbow builds: ursacomputing/crossbow @ actions-d485738cc1

Task	Status
homebrew-cpp

[HyukjinKwon]

@github-actions crossbow submit homebrew-cpp

[github-actions]

Revision: 70ff052

Submitted crossbow builds: ursacomputing/crossbow @ actions-652b58c285

Task	Status
homebrew-cpp

[github-actions]

⚠️ GitHub issue #48824 has been automatically assigned in GitHub to PR creator.

[github-actions]

⚠️ GitHub issue #48824 has no components, please add labels for components.