Launch Claude Code with Remote Control and surface the real session URL

[suleimansh]

Part of #209. Follow-up to #212 (which defaulted the dashboard link to the claude.ai/code list).

To give a true deep link to the live session, drive Claude Code with Remote Control enabled (--remote-control / a recognizable --name) and capture the real session URL Claude Code emits, then surface that on the dashboard instead of the generic list link.

Gated: Remote Control needs a claude.ai subscription (no API keys) and Claude Code v2.1.51+, and is opt-in, so this must degrade gracefully when unavailable (fall back to the #212 default). Pins this path to Claude Code; a Codex path is separate.

[suleimansh]

Raising priority: after the sync this is the real remaining MVP piece, not a nice-to-have.

With web-first = dashboard + Remote Control (see #165), showing the live session is what makes the web surface useful, and this is the piece that does it. Still infra-gated (a claude.ai subscription + Claude Code v2.1.51+ to test against), and it degrades to the #212 default (the claude.ai/code list) when unavailable. Build when we have a subscription to verify against.

[suleimansh]

De-risked against Claude Code 2.1.201 before building. Capturing a real Remote Control session URL from our runs is infeasible, on three independent walls:

1. Architecture. Our driver runs Claude Code headless (-p --output-format stream-json) to feed the dashboard. Remote Control is interactive-only; the same claude process can't be both.
2. No machine-readable URL. Headless -p + --remote-control silently ignores the flag and emits only a local UUID session_id, no claude.ai URL. Interactively, the URL is TUI-rendered only, with no --output-format seam to parse.
3. Auth model. claude remote-control refuses automation credentials: "requires a full-scope login token; long-lived tokens (setup-token / CLAUDE_CODE_OAUTH_TOKEN) are inference-only." That's exactly what a framework run uses.

So Remote Control is a user-initiated steer handoff, not something our headless orchestrator can drive or deep-link into. Closing as infeasible-as-framed.

The honest reframe is #221 (PR #222): label the default link "Open Claude Code" instead of "live session", keep the real session id, and document the claude auth login + --remote-control --name steer path in the README.