[FEATURE] Save conversation to local file (markdown/JSON export)

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

Conversations in the Claude desktop app (Chat and Cowork) are stored in a binary IndexedDB database that cannot be read or searched outside the app. There is no way to export, archive, or auto-save conversations as readable files. This makes it impossible to keep a personal archive, reference past chats in other tools, or move context between Claude Code, Chat, and Cowork.

Proposed Solution

Add an option in Settings to auto-save conversations as local files (markdown or JSON) to a user-specified folder. Ideally this would happen automatically when a conversation ends. A manual "Save conversation" button would also be helpful. This would apply to Chat, Cowork, and Claude Code so conversations can be accessed, searched, and shared across all three environments.

Alternative Solutions

I set up a workaround using Claude Code hooks and a Python script to save Claude Code sessions automatically. However there is no equivalent hook system for the Claude desktop app (Chat/Cowork) since it is a protected Windows app with no plugin system.

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_