Remote Control session confirmed active but never resolves — session lookup fails on claude.ai/code

## Description

`/remote-control` reports the session as active and gives a `claude.ai/code/session_...` URL, but the session never shows up as reachable from a paired mobile device, and visiting the URL directly does not find the conversation.

## Steps to reproduce

1. Run `/remote-control` in a Claude Code CLI session on desktop (Linux).
2. CLI confirms: `/remote-control is active · Continue here, on your phone, or at https://claude.ai/code/session_`
3. Open the Claude iOS app (same account) — the session does not appear in the Remote Control session list.
4. Visit the given `https://claude.ai/code/session_` URL directly in a browser — it connects/authenticates to claude.ai fine, but the specific conversation is not found.

## What I tried (none of it changed the outcome)

- Updating the iOS app
- Logging out and back into the iOS app
- Re-scanning the `/remote-control` QR pairing code
- Starting a brand-new terminal session and running `/remote-control` fresh
- Re-authenticating Claude in the browser

## Additional diagnostic

From within an active Claude Code session, listing peer sessions shows the newly-started session registered as plain `interactive` rather than `Remote Control`, even several minutes after the CLI confirmed `/remote-control is active` with a working URL — i.e. the desktop side reports active pairing, but that status is never reflected in the session list or resolvable by ID.

This points to a server-side session-registry/lookup issue (the session gets marked active and handed a URL, but isn't properly indexed for lookup afterward) rather than a client-side (iOS app) display bug, since a direct browser visit to the URL also fails to find the conversation.

## Environment

- Desktop: Linux (Claude Code CLI)
- Mobile: Claude iOS app, up to date
- Account has previously paired both mobile and desktop successfully (this is a regression, not a first-time setup issue)

Start at the `/remote-control` CLI entry point and trace how the active session receives its `claude.ai/code/session_` URL. Compare that path with the peer-session listing and session lookup behavior described in the report. Done means a newly activated session appears as Remote Control, is listed on the paired iOS device, and resolves from the URL.

索引モデルが issue の本文から書いたものです。