Nope only the message content is encrypted. So what they have unencrypted is of course your personal information (phone number etc), all your contacts, and the list of all messages sent (datetime, and contact or contacts). This enable them to have a great social map that evolves after each message sent
And that is if the encryption remain unbroken. Don't forget that the NSA has a history of placing backdors in cryptography schemes (like that mathematically flawed key based on a weak elliptic curve, standardized and approved by the NSA after they found their exploit)
Thank you for that info and the link I'll go into that. Just to summarize, if you have the knowledge and time: this is at-rest encryption? I'm not sure how it could be end-to-end encryption and at the same time enable to start new conversations with other Signal users / discovery based on name / phone number