You haven’t explained why I have to choose between these two trade-offs. I want neither: I want strong metadata protection without being forced to link my account to my real-world identity.

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.

It’s already a problem that it sends the client’s version, device details, avatar, and bio at all. Those device details are transmitted during federation along with everything else.

https://spec.matrix.org/latest/server-server-api

signal done it pretty well

Signal is free from this disaster, and client version and device details are only visible to the main server — not to mention the avatar, name, and many more items listed above being in plain text.