option: "allow customer to choose a specific person for the booking" option does not seem to work

Your expectation is correct: Microsoft documents that disabling staff selection removes the customer’s ability to choose a person, with Bookings assigning an available staff member instead. “Optional” means the visitor can skip choosing; it does not mean selection is disabled.

The first screenshot shows the default scheduling policy. Check the “1hr Discovery meeting” service under Services as well. Microsoft documents that a service-level scheduling policy takes precedence over the business-level policy, so the page default may not be the effective setting for that service.

Open that service, inspect its staff-selection setting and whether it uses the default scheduling policy, then disable selection at the effective level and save. Retest the public link for that same service in a private browser session.

If the selector remains despite the service’s effective setting being disabled, capture both configurations and the public result for Microsoft support. That would establish a specific reproducible inconsistency.