I have had a customer request that there be an option to have a public repository but only have internal users (users who have been granted access to Bitbucket and then project/repository) as reviewers where only they can approve/reject and merge.

The customer understands that public users can not merge PR, but they are wanting a feature for the public logged-in Bitbucket user not having the capability to review (Approve/ Request Changes/decline and so on).