I started keeping my chat history files since it's easier and faster to search through them vs opening old chats directly from Cursor/VSC. After trying the Codex extension, then looking for how to export Codex's tasks/chat history, I found that the Codex extension has no export.
The Codex extension creates rollout.jsonl files and that's it. Today, I even had Cursor open and the Codex extension suddenly refused to show me any of the tasks history any more, even though the .jsonl files were still where they always were.
I made JsonlToMD to process the rollout.jsonl into markdown so I can keep my own chat history in markdown format. I added useful command line switches for flexiblity. It's written in C# and it uses NO dependencies so it is super lightweight and completely cross-platform Mac/Windows/Linux.
Share and enjoy!