Does 'Composer' retain 'Composer Chat' history?

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)