[FEATURE] Export a chat from one project to another project

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

It would be useful to export a Claude Code conversation from one project and import it into another. This would help when:

Migrating work between repositories (e.g., monorepo restructuring, forking)
Sharing debugging context or architectural decisions with a teammate working in a different project
Continuing a line of investigation that spans multiple codebases

Proposed Solution

A command like /export that saves the conversation to a portable file (e.g., JSON or Markdown), and a corresponding /import or --import flag to load it as context in a new project session.

Alternative Solutions

Manually copying relevant info into CLAUDE.md or memory files — works but is lossy and tedious
Re-explaining context from scratch in the new project — time-consuming and error-prone

Priority

Medium - Would be very helpful

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_