Normally, when a booking is made on the booking page, the appointment is linked to the calendar specified in "Calendars to add" as public to the members.

If the project setting is Private, the appointment in Google Calendar may become Private when you create a booking on the booking page.

When creating an appointment in a public calendar, the project must be made public to the entire team, or the project must be unlinked from the booking page.

*After the settings are changed, the changes will be reflected from newly created appointments.

Edit Booking Page > Team Booking Request > Project