If I meet & greet with multiple sitters before booking, once I have 'officially' booked with one of them, will rover notify the unbooked sitters, or is that my responsibility?

As a sitter, I am understanding when a client wants to meet&greet multiple sitters and does not choose me. I am really appreciative of a message letting me know, so that I can archive the request. If the sitter is waiting on you to confirm the booking and hasn't archived the request, then their calendar will be marked unavailable for the dates of the request. So the sitter who is upset may have lost a booking or even two bookings because you did not let her know in a timely manner.

It comes down to personal preference, I think. Though I would say that it's polite to end the Rover conversation just like you would a face-to-face conversation. As in, don't leave any questions hanging, say thanks or no thanks and clarify that the interaction is over. No one gets any information automatically through Rover. All communication is up to the client and the sitter.

It's very kind if you send a message to the sitters along the lines of nice meeting you, maybe I can work with you in the future. In reality, most people don't do that. Rover doesn't notify those who weren't booked. Most sitters know that Rover encourages multiple sitter meet&greets to find what you think is the best match. On the flip side of the coin, the sitter also could have messaged you and asked if you were planning on confirming the booking. The sitters not booked really should not get very upset, maybe just a little disappointed. Anything more than that seems unprofessional.

Is she upset about not being picked, or about not being notified?

No rover will not notify if you decide not to book a sitter. In the future you should thank them for the meet and greet and let them know that you’ve picked someone else.

It can actually hurt their business if they are just waiting around for you, because from what I’ve read it seems that once a request is made it can take you out of search results for that time because of the potential booking. So it’s best to let them know so they can archive the request.