Matrix can expose your device name and device details to other homeservers through federation. Profile information such as your avatar and bio can also be queried remotely. A client version is not a dedicated federation field, but it can leak through the device name. Signal at least has Sealed Sender, which hides the sender's identity from its own service in supported cases.
This is about metadata, not centralisation, self-hosting, or phone-number registration. Those are separate issues, not trade-offs.