ask the agent what it is still running

Officer's session records are in memory and die with `pm2 restart officer`, while the agent is a PM2
peer and keeps generating. `adoptOrphanedSession` rebuilds a binding — but only when a browser
reconnects to a session *by id*, which you can only do if you already knew the id. So a session that
survived a restart was invisible, and nothing could answer "what is running right now".

`claude:list` returns each live session with `isGenerating` and `pendingTasks` — the same two fields the
agent's own `armIdle` consults before collecting a session, so a caller can tell "busy" from "merely
open" the way it does. Surfaced as `GET /chat/live`, which sits beside `/chat/sessions`: those are
transcripts on disk, these are the ones with a process behind them.

`getActiveSessionKeys` is replaced rather than joined. It returned bare keys, could not distinguish a
session mid-turn from one merely open, and had never been called by anything.

`listLiveClaudeSessions` fails toward EMPTY, where `isClaudeGenerating` beside it fails toward alive.
The asymmetry is deliberate: not knowing there means leaving a spinner up, and not knowing here would
mean inventing sessions.

Step 2 of docs/chat-session-lifetime.md.

Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>

src/servers/sidecar-registry.ts

@@ -6,6 +6,7 @@ import type {
   ClaudeSpawnParams,
   ClaudeSpawnStreamingParams,
   ClaudeCodeResult,
+  LiveClaudeSession,
   OpenCodeRunParams,
   VncStartParams,
 } from './sidecar/protocol';
@@ -307,6 +308,31 @@ export function interruptClaude(sessionKey: string): void {
  * it is still typing is worse than leaving a spinner up a little longer. Only a registered agent that
  * says "no", or no agent at all, counts as dead.
  */
+/**
+ * Every session the agent is holding IN MEMORY right now — distinct from `listClaudeSessions` in
+ * `api/chat/claude-sessions`, which lists conversations from transcripts on disk. Those are the history;
+ * these are the ones with a process behind them.
+ *
+ * Officer's own session records live in memory and die with `pm2 restart officer`, while the agent — a
+ * PM2 peer, not a child — keeps running and keeps committing to chat_session_events. Until this existed
+ * a surviving session was invisible: `adoptOrphanedSession` only fires when a browser reconnects to one
+ * *by id*, so nothing could answer "what is still running".
+ *
+ * Fails *toward empty*, unlike `isClaudeGenerating` which fails toward alive. The asymmetry is
+ * deliberate: there, not knowing means leaving a spinner up; here, not knowing would mean inventing
+ * sessions, and an enumeration that reports things that may not exist is worse than a short one.
+ */
+export async function listLiveClaudeSessions(): Promise<LiveClaudeSession[]> {
+  const sc = findSidecarByCapability('claude');
+  if (!sc) return [];
+  try {
+    const res = await sendCommandToSidecar(sc, { type: 'claude:list', id: nextId() });
+    return res.type === 'claude:sessions' ? res.sessions : [];
+  } catch {
+    return [];
+  }
+}
+
 export async function isClaudeGenerating(sessionKey: string): Promise<boolean> {
   const sc = findSidecarByCapability('claude');
   if (!sc) return false;