Booking an appointment - blocking other services

Is it possible to set the configuration so that if we have e.g. 10 services (types of haircuts, e.g. short, long, wedding hairstyle, etc.), but one service person (e.g. hairdresser) - each service is configured as a separate product. If a customer chooses to book an appointment for a given hour, are other products blocked for that hour?
If it doesn't work, this system has very big limitations - because with 10 services, 10 people would have to be employed :(

By the way - the date selection does not work when I want to block a date for a selected service in the calendar in the backend. The date field in the calendar is inactive.

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