Show whether session was started by daemon or terminal

[HirokiKobayashi-R]

Problem

When looking at the session list on the phone, there's no way to distinguish between:

• Sessions started directly from the terminal (startedBy: 'terminal')
• Sessions spawned by the background daemon (startedBy: 'daemon')

This makes it difficult to manage sessions — users can't tell which ones they're actively running in a terminal vs which ones are running headlessly via the daemon.

Context

The CLI already sends metadata.startedBy ('terminal' | 'daemon') to the server when creating a session. This field is available in the app's session data but is not currently displayed anywhere in the UI.

Proposed Solution

Append a label to the session subtitle (the path line) when the session was started by the daemon:

~/projects/my-app              ← terminal (no label needed, it's the default)
~/projects/my-app · daemon     ← daemon-spawned

This is a minimal change to getSessionSubtitle() in sessionUtils.ts.

Alternatives Considered

• Icon badge: Small icon next to session name (more visual, but heavier change)
• Color bar: Colored left border on session card (requires style changes)
• Section separation: Separate "Active" and "Daemon" groups (largest UI change)

The text label approach is the least invasive and most informative.