"Server-side" is a bit of a misnomer here.
Sure, for e.g. E2E email, the expectation is that all the computation occurs on the client, and the server is a dumb store of opaque encrypted stuff.
In a traditional E2E chat app, on the other hand, you've still got a backend service acting as a dumb pipe, that shouldn't have the keys to decrypt traffic flowing through it; but you've also got multiple clients — not just your own that share your keybag, but the clients of other users you're communicating with. "E2E" in the context of a chat app, means "messages are encrypted within your client; messages can then only be decrypted within the destination client(s) [i.e. the client(s) of the user(s) in the message thread with you.]"
"E2E AI chat" would be E2E chat, with an LLM. The LLM is the other user in the chat thread with you; and this other user has its own distinct set of devices that it must interact through (because those devices are within the security boundary of its inference infrastructure.) So messages must decrypt on the LLM's side for it to read and reply to, just as they must decrypt on another human user's side for them to read and reply to. The LLM isn't the backend here; the chat servers acting as a "pipe" are the backend, while the LLM is on the same level of the network diagram as the user is.
Let's consider the trivial version of an "E2E AI chat" design, where you physically control and possess the inference infrastructure. The LLM infra is e.g. your home workstation with some beefy GPUs in it. In this version, you can just run Signal on the same workstation, and connect it to the locally-running inference model as an MCP server. Then all your other devices gain the ability to "E2E AI chat" with the agent that resides in your workstation.
The design question, being addressed by Moxie here, is what happens in the non-trivial case, when you aren't in physical possession of any inference infrastructure.
Which is obviously the applicable case to solve for most people, 100% of the time, since most people don't own and won't ever own fancy GPU workstations.
But, perhaps more interesting for us tech-heads that do consider buying such hardware, and would like to solve problems by designing architectures that make use of it... the same design question still pertains, at least somewhat, even when you do "own" the infra; just as long as you aren't in 100% continuous physical possession of it.
You would still want attestation (and whatever else is required here) even for an agent installed on your home workstation, so long as you're planning to ever communicate with it through your little chat gateway when you're not at home. (Which, I mean... why else would you bother with setting up an "E2E AI chat" in the first place, if not to be able to do that?)
Consider: your local flavor of state spooks could wait for you to leave your house; slip in and install a rootkit that directly reads from the inference backend's memory; and then disappear into the night before you get home. And, no matter how highly you presume your abilities to detect that your home has been intruded into / your computer has been modified / etc once you have physical access to those things again... you'd still want to be able to detect a compromise of your machine even before you get home, so that you'll know to avoid speaking to your agent (and thereby the nearby wiretap van) until then.