As everyone probably already know, cursor is not really local first, a pretty significant part of logic is in their server env, yet their local storage still can provide some information. Their data are spread between SQLite and JSONL, depending on whether you use a dev server or container you may have various level of informations

Claude code on the other side is much more cleaner, also made build tool on top of it really easy. I have a deep dive in Claude code local sessions as well, I believe many people have done it already