Remote control: app shows stale sessions and does not display currently active session

Preflight Checklist

• [x] I have searched existing issues and found no exact match
• [x] I can reproduce this bug consistently

Bug Description

When using the remote control feature to view Claude Code CLI sessions from the Claude app, two issues occur simultaneously:

1. Stale sessions persist in the app -- Previously terminated CLI sessions continue to appear in the app session list
2. Active session not visible -- The currently running CLI session does not appear in the app, making it impossible to connect to it

The app session list becomes out of sync with the actual state of CLI sessions.

Steps to Reproduce

1. Start a Claude Code CLI session (terminal)
2. Open the Claude app and check the remote control / Code tab
3. End the CLI session (Ctrl+C or /exit)
4. Start a new CLI session
5. Check the app again -- the old session still appears, but the new active session may not show up

Expected Behavior

• Terminated sessions should be removed from (or marked as inactive in) the app session list
• The currently active CLI session should appear in the app promptly

Environment

• Claude Code version: 2.1.70
• OS: macOS (Darwin 24.6.0, arm64)
• Note: ~/.claude/session-env/ has accumulated 1,097 session entries, which may be a contributing factor

Related Issues

• #28917 -- Feature request to manually revoke stale remote control session links
• #23530 -- Stale session list in /resume command (different feature, similar symptom)