What happens after the booking?
A booked meeting does not end the relationship. If the prospect does not show up, the AI gets back in touch without blame and offers a new time. If the event is cancelled, it acknowledges it and offers to rebook. If the prospect writes again to move the meeting, the request comes back to you in the inbox, so no reschedule gets lost.
Scheduled messages prepare the meeting or keep what follows moving: sending the promised resource, recalling the next step. They are written at send time, from the real conversation, and never go out on top of a conversation waiting for a reply.
If you also use WhatsApp, messages around the meeting can go out on that channel once the prospect has shared their number.