Remote/mobile session list lacks distinguishing info between sessions

Problem

In the Claude mobile app's remote control session list, multiple sessions on the same machine are nearly indistinguishable. Sessions display only:

• Auto-generated name (if the conversation has progressed enough) OR the profile type ("Personal" / "Work")
• Machine name (e.g., "GARETT-PC")

When a user has multiple sessions under the same profile on the same machine, the list shows identical entries like:

Personal
  GARETT-PC

Personal
  GARETT-PC

There is no way to tell which session is which without opening each one and asking.

Impact

• Users must tap into each session to identify it, breaking flow
• With 3+ sessions this becomes a guessing game
• Particularly painful on mobile where switching between sessions is slower

Suggested approaches

• Show the working directory (or its basename) as a subtitle under the session name
• Show a timestamp of last activity
• Allow users to set a persistent session label/icon from within the session
• Auto-generate names earlier in the session lifecycle (currently only happens after substantive conversation)

Related issues

• #33527 — Auto-rename sessions based on conversation context (focused on terminal tabs)
• #32389 — Session Notes — editable description/notes field

Both are related but focus on the terminal experience. This issue is specifically about the remote control list view in the mobile app, where the lack of distinguishing info is most acute because there's no terminal title bar or tab to fall back on.

Environment

• Remote control via Claude mobile app (iOS)
• Multiple concurrent sessions on one Windows machine