Your favourites are private to your account. An owner sees the number of people who saved a listing in their analytics, and nothing about who they were.
What the business is told
A number in their analytics — how many people saved the listing. Never who, and never when an individual saved it.
What other users see
Nothing. Your favourites list is private to your account and is not shown on any public profile.
Favourites need an account because they have to be stored against somebody. Signed out, there is nowhere to keep them.