Did you see that Claude Code just came out with "channels" that allows for messages to be injected into the session/sent out by claude via hooks and MCP server [1]? I had CC code an integration between fenced and CC using channels and it actually worked - a little clunky since there is no streaming, but very interesting nevertheless.
Right now this uses React for Web but could also see it in the terminal via Ink.
And I love the "freeze" idea — maybe then you could even share the mini app.