The official signal.org blog post I linked does actually explain how it works. They write that the client sends parts of hashed phone numbers to Signal:

> The client transmits those truncated hashes to the service. The service does a lookup from a set of hashed registered users. The service returns the intersection of registered users. The obvious problem with this method is that the hash of a user identifier can almost always be inverted. Regardless of whether the identifier is a phone number, a user name, or an email address, the “keyspace” of all possible identifiers is too small.

Also: Signal messages are currently never P2P. They always pass through Signal servers, which see (but apparently not retain) your IP and timing metadata. The Signal WebRTC calls are partially peer-to-peer, that is what the relaying in the Signal settings panel is about.