Revert "build: Move "Test plugin upgrades" to a post-build workflow"

[anomiex]

Changes proposed in this Pull Request:

This reverts commit 4883758.

It looks like GitHub has a fairly critical bug (which they've apparently
not cared about for 2 years) where the check run created from Actions
gets assigned to a random suite. If that random suite happens to be one
of the Gardening runs, it can get lost when the next Gardening run
happens.

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?

Jetpack product discussion

p1661807167941679/1661802332.889069-slack-CDLH4C1UZ

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

No

Testing instructions:

• Things should work as they did before.

[sdixon194]

rip

[github-actions]

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