Fix cleanup example to use pull_request_target trigger

[Mogyuchi]

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Why:

Closes: #31321

What's being changed (if available, include any code snippets, screenshots, or gifs):

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You may find it useful to copy this table into the pull request summary. There you can edit it to share links to important articles or changes and to give a high-level overview of how the changes in your pull request support the overall goals of the pull request.

Source	Preview	Production	What Changed
actions/using-workflows/caching-dependencies-to-speed-up-workflows.md	fpt ghec ghes@ 3.11 3.10 3.9 3.8	fpt ghec ghes@ 3.11 3.10 3.9 3.8

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fpt: Free, Pro, Team ghec: GitHub Enterprise Cloud ghes: GitHub Enterprise Server

[nguyenalex836]

@Mogyuchi Thanks so much for opening a PR! I'll get this triaged for review ✨

[Mogyuchi]

@jc-clark https://github.com/github/docs/pull/31582#issuecomment-1979764206

What would you think of keeping pull_request as the triggering event here but adding a note above the example that links to "pull_request_target" and describes the cross-repo pull request use case?

No… I think we should use "pull_request_target". Especially in public repositories, I think there is a possibility that cross-repo pull requests will be made even if the repository owner does not assume it. Therefore, I think we should present the example that takes into account the existence of cross-repo pull requests.

[jc-clark]

Closing this PR. See my comment here. Our team will make some improvements to this article internally.

Thanks everyone!