Feature request: Unified session history across CLI, Desktop app, VS Code, and Web

Currently, Claude Code sessions are siloed by client:

• Terminal CLI sessions don't appear in the Desktop app
• VS Code extension sessions are separate
• Web (claude.ai/code) sessions are isolated

There is no way to view all sessions from a single account in one place.

For comparison, OpenAI Codex syncs all sessions across its app regardless of where they were started.

Expected behavior: All Claude Code sessions tied to the same account should be visible and searchable from any client (Desktop app, CLI, VS Code, Web).

Why this matters: When working across multiple terminals, IDE, and desktop app throughout the day, it's difficult to find and reference past sessions.