[8.x](backport #40915) Chore: update packaging pipeline to run automatically on 8.x branch

[mergify]

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• My code follows the style guidelines of this project
• I have commented my code, particularly in hard-to-understand areas
• I have made corresponding changes to the documentation
• I have made corresponding change to the default configuration files
• I have added tests that prove my fix is effective or that my feature works
• I have added an entry in CHANGELOG.next.asciidoc or CHANGELOG-developer.next.asciidoc.

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This is an automatic backport of pull request #40915 done by [Mergify](https://mergify.com).

[mergify]

Cherry-pick of e8f41bb has failed:

On branch mergify/bp/8.x/pr-40915
Your branch is up to date with 'origin/8.x'.

You are currently cherry-picking commit e8f41bbb0f.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   .buildkite/packaging.pipeline.yml

no changes added to commit (use "git add" and/or "git commit -a")

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

[botelastic]

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