Desktop app: forked sessions don't auto-connect Remote Control despite "Enable remote control by default"

## Environment
- Claude Code 2.1.270, Claude Desktop app (macOS 15.7.3)
- Settings → Claude Code → **Enable remote control by default** is ON
- Pro/Max subscription login

## Steps to reproduce
1. In the desktop app, start a session. It auto-connects Remote Control and appears in the Claude mobile app as expected.
2. Fork that session (desktop app fork).
3. Work in the fork for a while (multiple turns).
4. Open the Claude mobile app → Code → session list.

## Expected
The forked session appears on mobile like any other session, since auto-connect is enabled.

## Actual
The fork never appears on mobile. Only sessions that were started fresh (not forked) are listed. Cross-session `ListAgents` from another session shows the forks as plain local `interactive` sessions with no Remote Control registration.

Running `/remote-control` manually inside the fork fixes it — but on the first attempt it returned:

> remote control requires an active session, send a message first

even though the fork had been actively working for hours. Sending another message and re-running `/rc` after the reply then connected it successfully.

## Notes / guess
Auto-connect seems to fire on process start, and a fork appears to reuse the parent's already-running process, so the hook never fires for it. The "requires an active session" error on a session that clearly *is* active is probably the same root cause (the fork isn't seen as a distinct registrable session until it's poked).

Workaround for anyone hitting this: fork → type `/rc` once (send a message first if it complains).

Start by tracing the /remote-control and /rc entry points, then inspect how cross-session ListAgents represents forked sessions. Reproduce the fork workflow and verify that a fork auto-registers for Remote Control without requiring an extra message or manual command, while fresh sessions continue to connect normally.

Written by the indexing model from the issue text.