I’m really interested in this history issue. Not trusting my logs will persist really gets in the way moving quickly with Cursor and building apps to the level of complexity I want.
I’ve been working with a small team on a tool (SpecStory Cursor Extension) that makes it possible to save Composer history. We export the history as Markdown, and also display it in a browser view with a shareable URL. This all towards the goal of being able to work freely with the chat & Composer — to make use of this both for myself, and for maintaining a useful context.
(More here: Built a Cursor Extension to save and share chat and composer history)