[META] Enhance repository backport PRs with Autoapproval and Automerge

[peterzhuamazon]

This is a meta issue to extend the support of autoapproval and automerge on backport PRs.

We have done a pilot run of this feature on documentation-website repo with:

• Auto-merge Backport PRs in documentation-website repo documentation-website#6400

The implementation at the time is using shell scripts combined with two existing workflows:

• https://github.com/VachaShah/backport
• https://github.com/pascalgn/automerge-action

We want to implement new features either in the existing backport workflow, or better, utilizing the existing app created for backport, the https://github.com/organizations/opensearch-project/settings/apps/opensearch-trigger-bot.

Similar to:

• Automation process to handle issue transfers between opensearch-project repos. #4505
• [META] Documentation website enhancements w/ engineering support #4455

This app currently is only used for token retrieval, and did not setup the probot framework as well as webhook callbacks. It is better to implement those in a push event instead of using the existing automerge pull event trigger.

Thanks.

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Acceptance Criteria:

• Use GitHub App to replicate behaviors in Auto-merge Backport PRs in documentation-website repo documentation-website#6400
• Make sure to use a combination of triggers such as label + comment by maintainer(s) to enable the automerge
• Make sure to have the code maintained in a centralized place for easier deployment to all corresponding repositories
• Have GitHub App installed on the org level