[FEATURE] Sync conversation history across Claude Code and claude.ai

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

Claude Code sessions are completely siloed from claude.ai and the Claude app. There's no way to search or retrieve terminal sessions from the app, or reference app conversations from Claude Code.

Proposed Solution

Unified history/search across all Claude surfaces or the ability to search Claude Code sessions from the app and vice versa.

Alternative Solutions

_No response_

Priority

High - Significant impact on productivity

Feature Category

API and model interactions

Use Case Example

I use Claude Code every day for research building reasoning pipelines, debugging, running experiments. Then I switch to the app to brainstorm or revisit ideas when I'm not at my terminal. The problem is these are completely disconnected. If I spent 3 hours in Claude Code iterating on a some codebase, I can't reference any of that from the app. I have to re-explain everything from scratch. And when I go back to Claude Code the next day, it doesn't know what I discussed on the app either.

Additional Context

_No response_