For now there is no extension or builtin feature as far as I know which exports chats from other directories which you closed, you could though check the chat database (sqlite) in the application support directory if there are such entries. Just make sure to not open the db while cursor is open, you can back it up.
Opening Cursor in a different directory cant show the another directory’s chat, since its dependent on the active ‘project directory’. Though if you remember where it was open at begin it could be retrieved in Cursor if you open it that way again. (close all other instances)
Specstory has built an extension that actually does export the chat history while you are using Cursor, in the current project directory. That would help prevent the loss of next chats.