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GH-44657: [CI][Dev] Add write permission to the crossbow comment bot (#44658)

### Rationale for this change

It needs to write a comment to the target PR.

### What changes are included in this PR?

Add write permission to only the crossbow comment bot.

### Are these changes tested?

No.

### Are there any user-facing changes?

No.
* GitHub Issue: #44657

Authored-by: Sutou Kouhei <kou@clear-code.com>
Signed-off-by: Jacob Wujciak-Jens <jacob@wujciak.de>