Update example with Octokit Checks API methods

[matiasalbarello]

Octokit supports creating and updating checks by using create_check_run and update_check_run: https://rdoc.info/gems/octokit/Octokit/Client/Checks

Why: the example is outdated and the cited gem now supports appropriated methods.

What's being changed: use create_check_run and update_check_run of the used gem instead of post and patch to the API.

Check off the following:

• I have reviewed my changes in staging. (look for the deploy-to-heroku link in your pull request, then click View deployment)
• For content changes, I have reviewed the localization checklist
• For content changes, I have reviewed the Content style guide for GitHub Docs.

[welcome]

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[janiceilene]

@matiasalbarello Thanks so much for opening a PR! I'll get this triaged for review ⚡

[janiceilene]

It looks like our new action inadvertently closed this 🙃 Sorry about that! Reopening and triaging this for review 💛

[skedwards88]

Thank you for this update! I'll get it merged down for you.

[github-actions]

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