actions: Re-enable Post-Build stuff

[anomiex]

Proposed changes:

Now that we have it working, this undoes the changes from #28467 and #28502. The Post-Build workflow is now responsible for the plugin upgrades check, and the Slack notification has been updated to correctly handle being triggered by the Post-Build workflow.

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

None

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

No

Testing instructions:

• Merge then see if stuff works

[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 🤖

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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.

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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 you’ve done so, switch to the "[Status] Needs Review" label; someone from Jetpack Crew will then review this PR and merge it to be included in the next Jetpack release.

[github-actions]

Are you an Automattician? You can now test your Pull Request on WordPress.com. On your sandbox, run bin/jetpack-downloader test jetpack update/re-enable-post-build-stuff to get started. More details: p9dueE-5Nn-p2