Briar is designed to provide resilient communications, this includes sharing identifies necessary for local area networking. Because of this Briar has never had a goal to provide anonymity (see the Briar wiki: https://code.briarproject.org/briar/briar/-/wikis/FAQ#does-briar-provide-anonymity)
Anonymity is an explicit goal of Cwtch, as such the protocols have been designed to provide against that risk model (See the Cwtch handbook: https://docs.cwtch.im/security/intro)