docs: Update PR approval process to use GitHub's native review system

[timcoding1988]

Checklist

Ensure you have completed the following checklist for your pull request to be reviewed:

• Certify you wrote the patch or otherwise have the right to pass it on as an open-source patch by signing all
  commits. (git commit -s). (If needed, use git commit -s --amend). The author email must match
  the sign-off email address. See CONTRIBUTING.md
  for more information.
• Referenced issues using Fixes: #00000 in commit message (if applicable)
• Tests have been added/updated (or no tests are needed)
• Documentation has been updated (or no documentation changes are needed)
• All commits pass make validatepr (format/lint checks)
• Release note entered in the section below (or None if no user-facing changes)

Does this PR introduce a user-facing change?

None

[packit-as-a-service]

[NON-BLOCKING] Packit jobs failed. @containers/packit-build please check. Everyone else, feel free to ignore.

[Luap99]

I don't think that is a good advice, new people have no idea who to request and I rather not want them request me all the time. I think we do not need to mention this, reviewers are supposed to check on PRs themselves

[timcoding1988]

removed this.

[mheon]

Maybe mention tagging containers/podman-maintainers in a comment instead?

[Luap99]

Does this works? I think teams cannot be pinged as outside person (likely due spam problem)

Organization members can send a notification to an entire team by mentioning the team's name. Teams can only be made up of members of your organization, outside collaborators are unable to be on a team.

Visible teams can be viewed and @mentioned by every organization member.

https://docs.github.com/en/organizations/organizing-members-into-teams/about-teams

If you are not logged in you do not see the team mention as clickable, i.e. just log at this PR in incognito tab and look at the first packit comment

[Luap99]

Please do no use ci skip for this, simply just lets never use it. We need spellcheck and other basic things to always run.

[timcoding1988]

Please do no use ci skip for this, simply just lets never use it. We need spellcheck and other basic things to always run.

@Luap99 sure. re-commit this so it will trigger the whole flow

[TomSweeneyRedHat]

All kinds of Red Unhappy tests here @timcoding1988

[timcoding1988]

All kinds of Red Unhappy tests here @timcoding1988

@TomSweeneyRedHat rebased my branch. pr should be good

[mheon]

LGTM

[Luap99]

LGTM