[FR] Log Claude Code message when using the Cursor extension

[jverre]

Context

The Cursor extension logs in the background all Cursor chats to Opik so you can keep track of your LLM chats. Given the popularity of Claude Code, it would be create to log these chats to Opik as well

Implementation consideration

All Claude chats are stored locally in ~/.claude/projects, we can use a similar approach to how we implemented the Cursor chat logging.