Actually I myself cloned ChatSecure iOS, built it, and played it for a while. It's a nice app with elegant interface yet lacks push notification. If you plan to improve it, I would be happy to be a beta tester :-)
p.s.
So honest is this app to explicitly state that I need to keep it foreground to receive new message from XMPP server.
Sure, push notification needs a central server. But guys, we so badly need a mobile IM that meets similar security standards as this project. Do it, and the world will honor you.
Should the central server be the only missing component of a reliable, secure-paranoid, mobile IM system, I would be happy donating some dollars.
Because in people's experience, LLMs are often correct.
You are right LLMs are not authoritative, but people trust it exactly because they often do produce correct answers.