[FEATURE] Desktop: see the status of many sessions at once, without filtering

Related to #88020, but a different problem. That one is about arranging panes. This one is about seeing status without opening anything.

**What I do**

I run about 30 Claude Code sessions in parallel, every day, for work.

**The problem**

Today the desktop app gives me two ways to see session state:

- Split view, which shows **two** sessions: *"To view two sessions at once, hold Cmd on macOS or Ctrl on Windows and click a session in the sidebar."*
- Sidebar filters: *"filter sessions by status, project, or environment"*

Both are **pull**. I have to decide to look, then filter, then read the list. With 30 sessions I do that many times an hour, and most of the time the answer is "nothing needs me yet".

What I want is **push**: the state of all sessions visible at the same time, without any action from me. Then I only move when something changes.

**What I would like**

A compact status view of all sessions in one screen. It does not need to show the transcripts. It needs one row or one tile per session with:

- which state it is in (working / waiting on you / done)
- the project or worktree
- how long it has been in that state

Colour is enough for the state. Reading text is what I am trying to avoid.

**Why the count matters**

At 2 to 5 sessions, cycling with Ctrl+Tab is fine. At 30, the cost is not switching, it is **not knowing which one to switch to**. The sidebar can list them, but a list of 30 rows still has to be read.

**On the time part**

"How long it has been in that state" is the one I miss most. A session that has been working for 6 hours and a session that started 10 minutes ago look the same today. Once I had an agent rewriting and rerunning the same tests for most of a week and I did not notice, because it kept reporting progress. Elapsed time would have shown it in one glance.

Start by reviewing the desktop app's existing split view, sidebar session list, and status filters to understand how session state is presented. A complete change would provide a compact view showing every session's state, project or worktree, and elapsed time in that state without requiring filtering or opening sessions.

Written by the indexing model from the issue text.