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GH-34381: [Dev] Retrieve committers from arrow-site committers.yml instead of relying on author_association (#34557)

### Rationale for this change

If a committer has their ASF role on GitHub as private the GitHub PR bot author_association is not correctly assigned.

### What changes are included in this PR?

 This change uses the committers list on the arrow_site repository to retrieve the list of committers.

### Are these changes tested?

There is a unit test and have tested the different steps of the workflow individually but haven't tested the full workflow.

### Are there any user-facing changes?

No
* Closes: #34381

Lead-authored-by: Raúl Cumplido <raulcumplido@gmail.com>
Co-authored-by: Sutou Kouhei <kou@cozmixng.org>
Signed-off-by: Sutou Kouhei <kou@clear-code.com>