ci: Fix e2e repository_dispatch run

[anomiex]

Proposed changes:

During all the code rearranging in #32686, a piece of code that was only for workflow_run wound up being incorrectly run for repository_dispatch as well.

Other information:

• Have you written new tests for your changes, if applicable?
• Have you checked the E2E test CI results, and verified that your changes do not break them?
• Have you tested your changes on WordPress.com, if applicable (if so, you'll see a generated comment below with a script to run)?

Jetpack product discussion

#32686 (comment)

Does this pull request change what data or activity we track or use?

No

Testing instructions:

• Fork the repo, set necessary secrets, and trigger a repostory_dispatch.
  • Or look at https://github.com/anomiex/jetpack/actions/runs/6026033651 where I already did that. Note the jobs still failing there are an existing issue (e.g. see this past run from before Jetpack Boost: Split and Parallelize Jetpack Boost Tests #32686).

[github-actions]

Thank you for your PR!

When contributing to Jetpack, we have a few suggestions that can help us test and review your patch:

• ✅ Include a description of your PR changes.
  
• ✅ All commits were linted before commit.
  
• ✅ Add a "[Status]" label (In Progress, Needs Team Review, ...).
  
• ✅ Add testing instructions.
  
• ✅ Specify whether this PR includes any changes to data or privacy.
  
• ✅ Add changelog entries to affected projects
  

This comment will be updated as you work on your PR and make changes. If you think that some of those checks are not needed for your PR, please explain why you think so. Thanks for cooperation 🤖

---

The e2e test report can be found here. Please note that it can take a few minutes after the e2e tests checks are complete for the report to be available.

---

Once your PR is ready for review, check one last time that all required checks (other than "Required review") appearing at the bottom of this PR are passing or skipped.
Then, add the "[Status] Needs Team Review" label and ask someone from your team review the code. Once reviewed, it can then be merged.
If you need an extra review from someone familiar with the codebase, you can update the labels from "[Status] Needs Team Review" to "[Status] Needs Review", and in that case Jetpack Approvers will do a final review of your PR.