[8.13](backport #39297) Fix missing docker staging DRA artifacts

[mergify]

Proposed commit message

The DRA staging release is failing because the Buildkite step isn't capturing the right artifacts.
This commit fixes the issue by adjusting the artifact_paths to match the other steps.

Logs

Example of failure: https://buildkite.com/elastic/beats-packaging-pipeline/builds/96#018f2e52-8eda-4311-91fc-662353604f29

---

This is an automatic backport of pull request #39297 done by Mergify.

[mergify]

Cherry-pick of 85c9d14 has failed:

On branch mergify/bp/8.13/pr-39297
Your branch is up to date with 'origin/8.13'.

You are currently cherry-picking commit 85c9d146eb.
  (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/rm <file>..." as appropriate to mark resolution)
	deleted by us:   .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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[elasticmachine]

💚 Build Succeeded

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Build stats

• Start Time: 2024-04-30T11:43:40.536+0000

• Duration: 13 min 23 sec

Test stats 🧪

Test	Results
Failed	0
Passed	3
Skipped	0
Total	3

💚 Flaky test report

Tests succeeded.

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[dliappis]

Closing as it's been cherry-picked in #39198