Remote Control: sessions beyond the 6th are not visible/reachable in the mobile app

## Summary

When many Claude Code sessions are running concurrently with Remote Control enabled, only the first 6 sessions appear to be visible/reachable from the mobile app. The 7th session and beyond do not show up (or cannot be opened) on the phone, even though they are active on the desktop/CLI side.

## Environment

- Claude Code CLI: 2.1.251
- OS: macOS 26.5.2 (Darwin 25F84)
- Mobile app platform/version: not confirmed by reporter

## Steps to reproduce

1. Start more than 6 concurrent Claude Code sessions with Remote Control enabled.
2. Open the Claude mobile app and check the Remote Control session list.
3. Observe that only 6 sessions are listed/reachable; sessions beyond the 6th do not appear.

## Expected behavior

All active Remote Control sessions should be visible and reachable from the mobile app, up to whatever server-side capacity limit applies (server mode documents a `--capacity` default of up to 32).

## Actual behavior

Sessions beyond the 6th are not visible/accessible on the mobile client.

## Additional context

Could not find documentation of an intentional 6-session display limit. This may be a UI/pagination issue (sessions exist but aren't scrolled/paginated into view) rather than an intentional cap. Possibly related to the mobile session-visibility problems described in #80311, though that issue's symptom is different (dead sessions still shown as alive rather than a hard display cap).

Start by reproducing with more than 6 concurrent Claude Code CLI sessions with Remote Control enabled on macOS, then check the mobile Remote Control session list. Compare the observed cap with the documented server-mode --capacity default and related issue #80311. Done means sessions beyond the 6th are visible/reachable, or an intentional limit is clearly documented.

Written by the indexing model from the issue text.