chore: add diff check in migration post processing for kokoro repos

[GautamSharda]

Insert diff check logic to migrated repos to determine if kokoro tests should be run.

Some evidence that the diff check logic is added in the right place and works is that adding it to nodejs-logging-winston/trampoline_v2.sh and diff checking ./github/ results in:

(1) The tests are skipped / trivially passed when a PR does not make a change in ./github/: "no op" case

(2) The tests run when a PR makes changes in ./github/: "run tests" case

In our case, we diff check the package being migrated i.e., handwritten/{package_name} instead. Also, in our case, we have to account for firestore, which uses trampoline.sh (v1 / legacy) instead of trampoline_v2.

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• Make sure to open an issue as a bug/issue before writing your code! That way we can discuss the change, evaluate designs, and agree on the general idea
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• Appropriate docs were updated (if necessary)

Fixes b/478965516 🦕