Let Users Mark Important Context for New Chat

When starting a new chat based on the current one (e.g. after Cursor suggests “Start a new chat for better results”), allow users to indicate which parts of the current chat should be remembered or carried over.

Ideally, the user could specify this via a prompt, if supported.

This is especially helpful when recent changes are in obscure parts of the codebase—details that aren’t broadly relevant but occupy a lot of space in the chat context.