Overhaul the complete labelling system

[dhruvkb]

Fixes

Fixes #3823 by @dhruvkb
Fixes #4203 by @AetherUnbound
Fixes WordPress/openverse-infrastructure#740 by @dhruvkb

Description

This PR overhauls the complete labelling system to unify it in one place instead of the various disconnected systems.

Now the end-to-end labelling process is handled by the PR automations workflow.

Credits

Thanks to @GauranshMathur for bringing this up.

Checklist

• My pull request has a descriptive title (not a vague title likeUpdate index.md).
• My pull request targets the default branch of the repository (main) or a parent feature branch.
• My commit messages follow best practices.
• My code follows the established code style of the repository.
• I added or updated tests for the changes I made (if applicable).
• I added or updated documentation (if applicable).
• I tried running the project locally and verified that there are no visible errors.
• I ran the DAG documentation generator (just catalog/generate-docs for catalog
  PRs) or the media properties generator (just catalog/generate-docs media-props
  for the catalog or just api/generate-docs for the API) where applicable.

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[AetherUnbound]

These changes make sense to me, thanks for centralizing this all in one place! It'll be nice to have the labels apply equally across all PRs now 😄

[obulat]

LGTM! Nice to solve so many issues at once 🚀