I retried the download today and it works now without any extra steps on my part. I did update macOS — it’s possible that change helped. I’ll consider the issue resolved for now. I also submitted a bug report via Feedback Assistant (though I haven’t heard back yet).

I see issue in TestFlight log: A coordinated app install already exists with intent IXCoordinatorIntentUpdating (creator App Store) but request by appstoreagent was for intent IXCoordinatorIntentInitiating NSLocalizedFailureReason = Coordinated install exists with different intent.