Status line: sessions missing and Conductor sessions initially miscategorized as Terminal

Bug Description

Two related issues with the Claude Code desktop app status line:

1. Active sessions not showing in status line

When multiple terminal sessions and Conductor are running, the status line sometimes only displays one terminal session, omitting the others. This appears to be a recent regression — previously all active sessions were displayed correctly.

Expected: All active Claude Code terminal sessions and Conductor sessions should appear in the status line.
Actual: Only one terminal session is shown; other terminals and Conductor sessions are missing.

Screenshot (only one session visible despite multiple running):
!Screenshot 1

2. Conductor session initially categorized under TERMINAL

When a Conductor session starts, it initially appears under the "TERMINAL" section instead of the "CONDUCTOR" section. After about a minute, it correctly moves to the "CONDUCTOR" section.

Expected: Conductor sessions should immediately appear under the CONDUCTOR section.
Actual: Conductor sessions initially appear under TERMINAL, then move to CONDUCTOR after a delay.

Screenshots showing the transition:

• Before (mixed under TERMINAL): !Screenshot 2
• After (correctly separated): !Screenshot 3

Environment

• macOS (Darwin 25.3.0)
• Claude Desktop App v1.1.9493

Steps to Reproduce

1. Open multiple Claude Code terminal sessions
2. Start a Conductor task
3. Open the status line panel
4. Observe that some sessions may be missing
5. Observe that Conductor session initially appears under TERMINAL before moving to CONDUCTOR

🤖 Generated with Claude Code