No, not at all. If a server is AGPL-licensed, clients may have whatever license they want. If a client is AGPL-licensed, servers may have whatever license they want. What the AGPL does is provide that if code under the AGPL is used to provide network services, then clients of those servers are entitled to the server source code. You may read the terms here: https://www.gnu.org/licenses/agpl-3.0.en.html
There is no copyright mechanism by which the AGPL could apply to clients of an AGPL server.
What i’m saying about server code is the logic of agpl. GPL is about providing the means for users to obtain source code of the binary they’re running. There was a gap with api, where a given library feature could be exposed through network services and since no binary were downloaded then the code wouldn’t required to be open sourced. AGPL fixes that.
But we both agree that client code and server code are independent relative to their licensing terms.
e2e means server never does any encryption or decryption so i don't think they'll have any signal code running on their server.
They will however be required to open source their application code.
Edit : and i think open sourcing twitter app would be a stunning move, that elon is totally capable of.