I think I understand what went wrong. I was confused by the instructions and ChatGPT's UI.

I asked the GitHub app to review my repository, and the app told me to click the GitHub icon and select the repository from the menu to grant it access. I did just that and then resent the existing message (which is to be expected from a user). After testing a bit more, from what I understand, the updated setting is applied only to new messages, not to existing ones. The instructions didn't mention that I needed to repeat my question as a separate message again.