Link Claude Code sessions to CLAUDE.md for cross-device sync

Preflight Checklist

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• [x] This is a single feature request (not multiple features)

Problem Statement

Claude Code sessions started on desktop are not accessible via mobile app or mobile browser.
I would like the ability to view and continue Code sessions from mobile, started on desktop.

Proposed Solution

Claude Code sessions should be linkable to the repository's CLAUDE.md file. Since CLAUDE.md already serves as the context anchor for a project, it could also act as the identifier that groups all sessions for that repo under one entry in the user's claude.ai account accessible from any device.

Alternative Solutions

Use the repo URL as an identifier to group all sessions for the same project under one entry in the user's claude.ai account. CLAUDE.md could serve as the display name and context summary for that entry.

Priority

High - Significant impact on productivity

Feature Category

Other

Use Case Example

A developer starts a Claude Code session on their desktop to work on a project. Later they're away from their PC and want to check what was discussed or continue the conversation from their phone. Currently this is impossible, the session is stuck on the desktop. With repo-based sync they'd open claude.ai on mobile, see their project entry, and pick up where they left off.

Additional Context

Sessions already contain valuable project context, decisions made, code discussed, plans approved. Losing access when switching devices creates friction and forces users to either stay at their desk or repeat themselves in a new session.