There are several open protocols that meet your criteria that aren’t Matrix (with most of them using double-ratchet encryption similar to if not exactly like Signal). Due to server costs (Matrix eats a lot of RAM & storage), medium-sized entities usually bow out so the Matrix network largely consist of a few 1–10 user servers & massive centralization around Matrix.org & the hosted servers they provide. Since almost all the messages get synced to the Matrix.org server if just one Matrix.org user is in your room or whatever, all metadata will be synced to the mothership in Matrix.org that was originally funded by Israeli intelligence.
There are several open protocols that meet your criteria that aren’t Matrix (with most of them using double-ratchet encryption similar to if not exactly like Signal). Due to server costs (Matrix eats a lot of RAM & storage), medium-sized entities usually bow out so the Matrix network largely consist of a few 1–10 user servers & massive centralization around Matrix.org & the hosted servers they provide. Since almost all the messages get synced to the Matrix.org server if just one Matrix.org user is in your room or whatever, all metadata will be synced to the mothership in Matrix.org that was originally funded by Israeli intelligence.