Using the New Outlook for Mac features in business environments
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From what I research, Booking only has access to your primary calendar (your Exchange calendar when your account created).
So, in your case, a linked calendar (shared calendar) shows up in your account, but it is still a separated calendar, it is not your primary calendar. Booking will not be able to access to that linked calendar. Only when the event shows up in your primary calendar, Booking will show busy at the time.
I found this feedback that has the same idea as yours, please upvote for it.
Automatically block time in my calendar for appointments from shared calendars · Community
The more people upvote for it, the higher chance Microsoft will consider making it a feature.
I hope this information helps.
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