Session list: show status (running / waiting for input) and open PRs

Preflight Checklist

• [x] I have searched existing requests and this feature hasn't been requested yet
• [x] This is a single feature request (not multiple features)

Problem Statement

What I'd like

Two additions to the "Recents" session list in the Claude Code desktop app.

1. A status dot per session

Today the list is sorted by time only. There is no way to tell, at a glance,
whether a session is still running, has stopped, or is blocked on an answer
from me. I have to open each one.

Three states would already help a lot:

• running
• waiting for my input
• done / idle

The data is partly there already: list_sessions exposes isRunning. What's
missing is "the last turn was a question to the user". I realise that one is
the hard case — it will be wrong sometimes. Even shipping just
running/idle would be an improvement.

2. A filter or badge for sessions with an open PR

This one is a hard fact rather than a guess, so it should be reliable.
list_sessions already returns prNumber and prState.

My concrete case: a PR touching order execution sat open for 16 days across
sessions. Nothing in the UI surfaced it. A badge on the session row, or a
"has open PR" filter, would have caught it on day one.

Why it matters

I run several sessions in parallel across two projects. The cost of losing
track isn't cosmetic — in my case it's unmerged changes to money-handling
code drifting further from main every day.

Environment

Claude Code desktop app, Windows 11.

Proposed Solution

<img width="348" height="870" alt="Image" src="https://github.com/user-attachments/assets/fdaa9795-ace4-4b98-aa83-5c9b25a30523" />

Alternative Solutions

What I'd like

Two additions to the "Recents" session list in the Claude Code desktop app.

1. A status dot per session

Today the list is sorted by time only. There is no way to tell, at a glance,
whether a session is still running, has stopped, or is blocked on an answer
from me. I have to open each one.

Three states would already help a lot:

• running
• waiting for my input
• done / idle

The data is partly there already: list_sessions exposes isRunning. What's
missing is "the last turn was a question to the user". I realise that one is
the hard case — it will be wrong sometimes. Even shipping just
running/idle would be an improvement.

2. A filter or badge for sessions with an open PR

This one is a hard fact rather than a guess, so it should be reliable.
list_sessions already returns prNumber and prState.

My concrete case: a PR touching order execution sat open for 16 days across
sessions. Nothing in the UI surfaced it. A badge on the session row, or a
"has open PR" filter, would have caught it on day one.

Why it matters

I run several sessions in parallel across two projects. The cost of losing
track isn't cosmetic — in my case it's unmerged changes to money-handling
code drifting further from main every day.

Environment

Claude Code desktop app, Windows 11.

Priority

Critical - Blocking my work

Feature Category

CLI commands and flags

Use Case Example

_No response_

Additional Context

_No response_