Dispatch (Claude.ai desktop + iPhone) should surface existing local Claude Code sessions

Feature request

The Dispatch feature in the Claude.ai desktop and iPhone apps lets me drive my computer remotely from my phone, but it has no awareness of my existing local Claude Code sessions.

Current behavior

• Dispatch (iPhone + desktop) shows only sessions spawned from within Dispatch itself — in my case, a single long-running session.
• My local Claude Code sessions — both CLI-launched (claude in terminal) and desktop-app-launched — are completely invisible from Dispatch.
• Those local sessions number in the thousands, all stored at ~/.claude/projects/<encoded-cwd>/<uuid>.jsonl, and the CLI's claude --resume picker (with Ctrl+A) can list both kinds without issue.

Expected behavior

From Dispatch on my iPhone I'd like to either:

1. See and resume any existing local Claude Code session (CLI or desktop), or
2. At minimum, send a prompt into a specific local session by ID/name.

Use case: I'm away from my Mac and want to check in on or continue a specific in-flight session. Today the only path is "start a new Dispatch session," which can't see the work already running.

Related

• #57345 — Desktop app sidebar filters out CLI sessions; same family of cross-product session-visibility gap. The fix there (treat ~/.claude/projects/ as the unified store) would presumably extend here.