Remote Control: mobile session list shows stale content while a CLI session is actively running (recurring — see #31487, #30922, both auto-closed as dupes without a fix)

Preflight Checklist

• [x] I have searched existing issues and found no open, unresolved match — this exact bug has been filed at least twice before and both times auto-closed as a duplicate of the other, then auto-closed again for inactivity, with no actual fix landing. See #31487 and #30922.

Bug Description

Remote Control's mobile session list ("Code" tab) does not reflect the live state of an actively running CLI session on desktop. While a session is mid-conversation:

1. The user checks the mobile Remote Control / Code tab mid-session and finds the session's displayed title and last-activity timestamp already frozen at an earlier point — well before the current turn — even though the desktop session is actively running and shows "Connected • Remote control".
2. As an attempted fix, renaming the session on desktop does not resolve this: the new title does not propagate to the mobile view either.
3. As a result, a user checking Remote Control on mobile cannot tell which desktop session corresponds to their current work, and sees content/labels that no longer match what's actually happening — with no user-side action (including renaming) able to force a resync.

This is distinct from (but related to) the "stale/orphaned session" reports in #31487 and #30922 — in this case the session is not orphaned or terminated, it is actively running and receiving turns in real time on desktop, but the mobile-visible index for it does not update in step, before or after a manual rename attempt.

Steps to Reproduce

1. Start a Claude Code CLI session on desktop and continue an active conversation for an extended period (many turns).
2. Open the Claude mobile app's Remote Control / Code tab while the desktop session remains active and connected — observe the session card already shows a stale title and an old last-activity timestamp, not matching current conversation content.
3. On desktop, rename the session (e.g. via a session-title tool/command) as an attempted fix.
4. Refresh the mobile Remote Control view — observe the title and timestamp are still stale; the rename did not propagate.

Expected Behavior

• A session's title and last-activity timestamp should update on the mobile Remote Control view promptly (within the same session, without requiring the session to end/restart) as the underlying session progresses or is renamed.

Environment

• OS: Windows 10 Home 10.0.19045
• Claude app: Desktop (Windows), Remote Control to mobile

Related Issues

• #31487 — auto-closed as duplicate of #30922 without a fix landing
• #30922 — auto-closed for inactivity without a fix landing

Reopening this class of bug because the auto-close bot has repeatedly killed reports before an engineer looked at the underlying sync issue. Requesting this stay open until the mobile session index is confirmed to update live rather than on a lagging snapshot.