Create a burner account for email/calendar, that solves most of those problems. Nobody will care if the AI leaks that you have a dentist appointment on Tuesday.
But isn't the whole supposed value-add here that it gets access to your real data? If you don't want it to get at your calendar, you could presumably just not grant it access in the first place – no need for a fake one. But if you want it to automatically "book me a haircut with the same person as last time in an afternoon time slot when I'm free later this month" then it needs access to your real calendar and if attacked it can leak or wreck your real calendar too. It's hard to see how you can ever have one without the other.
