Why I'm I getting double-booked for the same time slot?

If clients are able to 'double-book' you for the same time slot, these bookings might be on a secondary calendar, OR the Google calendar connected to the Meeting Scheduler isn't your default calendar.

Meeting Scheduler only syncs with your default calendar. Once a time slot is booked through the Meeting Scheduler's booking link, it blocks off that time on your default calendar. The default calendar is usually the one associated with your default Google account.