The blog article you link I think implies you do not have your own VM. LLMs are stateless, the previous conversation is fed in as part of the prompt.
You send your message, which is E2E encrypted. The LLM runs in an environment where it can decrypt your message and run in through the LLM, then send a response to you. Then it gets the next user's message and replies to them.
The key part is that the LLM is running inside an encrypted environment not accessible to the host system, so no one can watch as it decrypts your message.
That's what I get from reading your links.