Feature request: Manage Claude Code / CLI conversation history from claude.ai browser interface

Problem

There is no way to view or manage Claude Code CLI and desktop app conversation history from the claude.ai web interface. CLI sessions are completely siloed from the browser experience.

Proposed Solution

Surface Claude Code / CLI conversation history in the claude.ai browser interface, allowing users to:

• Browse past CLI/desktop session history
• Search across conversations from all clients (web, CLI, desktop)
• Continue or review a CLI session from the browser
• Delete or archive old sessions centrally

Use Case

After a long coding session in the CLI, being able to review what was done, search for a specific decision or file change, or share a session link — all from the browser without needing the terminal open.

Relationship to Existing Issue

Related to #53286 (cross-client session sync between CLI and desktop app) — both stem from the same root problem: Claude Code sessions are not connected to the broader claude.ai account ecosystem.

Additional Context

Users already expect their claude.ai account to be a unified hub. Extending that to include Claude Code sessions would significantly improve the overall experience, especially for teams and power users managing multiple projects.