fix(core,client): keep sessions busy until their background work reports back - #60500

A session that moved a tool to the background now stays busy until that tool reports back and its turn finishes, instead of showing idle in between.
The server owns the busy state and reports it with the existing session.status event. Sessions with no background work go idle exactly as before. Stacked on #60497.

🔍 Origin: reported in #51810 and #56660

❌ Before

1. A session moves a slow tool to the background and its turn ends.
2. ❌ The active-session list and the app mark it idle, then running again when the tool's notice wakes it.
3. ❌ The "done" sound plays at the first idle, before the work is done.

✅ After

1. The server counts a session busy while it drains or while it owns backgrounded work that will report back and wake it.
2. It publishes session.status (busy / idle) only when that changes, routed by session so moves never misroute it. GET /api/session/active reports the same thing, so clients hydrate one value on reconnect.
3. ✅ The app, the client store and the mini TUI follow session.status; the done sound waits for idle. Older servers keep the old behavior.
4. Stop also cancels the session's own backgrounded work.

- busy = a turn is draining
+ busy = a turn is draining || backgrounded work will still wake the session
+ busy changes -> session.status { busy | idle }   (existing event, now emitted)
  job finishes -> its notice wakes the session -> released only after the wake (no idle blip)
  shell({ background: true }) -> detached, never holds the session (dev servers)
+ interrupt (no resume) -> also cancels held jobs

📊 Proof

New tests in core (status sequence with a slow notice, Stop, held/detached jobs, bus routing across a move), server (active list), client store and mini TUI.

👀 Read: packages/core/src/job.ts, holds/waking: a held job keeps counting until its notice has woken the session, so the session never blips idle in between. packages/core/src/session/execution.ts, refreshStatus. The rest is routine.

⚠️ Trade-off: #51810 and #56660 asked for explicit background shells to count. This PR keeps them out so a dev server can't hold a session forever. A shell that auto-backgrounds after its yield_after still counts until it finishes (Stop cancels it).