If you add a provider to your favorites on TER, does it notify them that you favorited them?

No, we aren’t notified. So your secret is safe.

I’ve experienced one review board that did alert the provider that I’d added her my favorites, this one a popular site useful in the Pacific NW area. In that case it worked out OK but it did give me a start when I rcvd a DM from the provider within a day. So TER’s policy is not universally held.