In some sense, no - the protocol protects the contents of your messages. In another sense, yes - a compromised server is much easier to collect metadata from.
Metadata, yes. Of course, the protocols, and thus all the inconveniences of the Signal app people constantly complain about, are designed to minimize that metadata. But: yes. Contents of messages, though? No.
If Signal, the service, was designed to minimize metadata collection, then why is it so insistent on verifying each user's connection to an E.164 telephone number at registration? Even now, when we have usernames, they require us to prove a phone number which they pinky-swear they won't tell anyone. Necessary privacy tradeoff for spam prevention, they say. This isn't metadata minimization, and telephone number is a uniquely compromising piece of metadata for all but the most paranoid of users who use unique burner numbers for everything.
This is the most-frequently-asked question about Signal, it has a clear answer, the answer is privacy-preserving, and you can read it over and over and over again by typing "Signal" into the search bar at the bottom of this page.
The answer is not privacy-preserving for any sense of the word "privacy" that includes non-disclosure of a user's phone number as a legitimate privacy interest. Your threat model is valid for you, but it is not universal.
The question you posed, how Signal's identifier system minimizes metadata, has a clear answer. I'm not interested in comparative threat modeling, but rather addressing the specific objection you raised. I believe we've now disposed of it.
I don't believe there has been any such disposition in this thread. There have been vague assertions that it's been asked and answered elsewhere. Meanwhile, the Signal source code, and experience with the software, clearly demonstrates that a phone number is required to be proven for registration, and is persisted server-side for anti-spam, account recovery, and (as of a few months ago, optional) contact discovery purposes.
