fix(bridge): forward Pi agent_end so the spinner stops at workflow completion

The FE derived 'working' purely as activeSession && !pendingWidget, so the
final workflow turn — the only one that ends without a follow-up gate —
left the spinner on forever (observed live: 21592s after F8 approve).

- SessionBridge maps Pi's agent_end -> SSE system_event {event: agent_end}
- PiProcessManager notifies the client (info error + synthetic agent_end)
  when the child dies unexpectedly; expected teardowns stay silent
- sessionStore tracks agentActive (on: user entry/text_delta/ui_request,
  off: agent_end); AppShell working now requires it; resume sets it
  optimistically

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

backend/src/bridge/session-bridge.ts

@@ -34,6 +34,11 @@ export class SessionBridge {
         this.fan({ type: "text_delta", text: m.text ?? "" });
       } else if (m.type === "system_event") {
         this.fan(m as ClientEvent);
+      } else if (m.type === "agent_end") {
+        // Fine turno di Pi (pi-agent-core agent-loop): e' l'unico segnale che il turno e'
+        // concluso. Senza inoltrarlo, il FE resta "working" per sempre quando il turno
+        // finisce senza un gate successivo (ultimo step del workflow).
+        this.fan({ type: "system_event", event: "agent_end" });
       }
       // altri method nativi (setStatus/setWidget) e altri eventi Pi ignorati in MVP
     });
@@ -43,6 +48,9 @@ export class SessionBridge {
 
   onClientEvent(cb: (e: ClientEvent) => void): void { this.cbs.add(cb); }
 
+  /** Eventi generati dal backend stesso (es. exit inatteso del child Pi), non da Pi. */
+  emitClientEvent(e: ClientEvent): void { this.fan(e); }
+
   respond(uiResponse: object & { id: string }): void {
     // Correla sull'id RPC di Pi; `value` porta l'uiResponse (con l'id del descriptor) cosi'
     // il check interno del gate (resp.id === descriptor.id) regge.

backend/src/pi/pi-process-manager.ts

@@ -70,7 +70,20 @@ export class PiProcessManager {
     const rt: SessionRuntime = { rpc, bridge, child };
     this.runtimes.set(sessionId, rt);
     // Identity-checked: a stale child's exit must not evict a newer runtime.
-    child.on("exit", () => { if (this.runtimes.get(sessionId) === rt) this.runtimes.delete(sessionId); });
+    // Expected teardowns (teardown()/respawn) delete the runtime from the map BEFORE the
+    // exit event fires, so reaching this branch with `rt` still mapped means the child
+    // died on its own: tell the client, or the UI spins forever waiting for a turn end.
+    child.on("exit", (code) => {
+      if (this.runtimes.get(sessionId) === rt) {
+        this.runtimes.delete(sessionId);
+        rt.bridge.emitClientEvent({
+          type: "info",
+          level: "error",
+          text: `Pi process exited unexpectedly (code ${code ?? "?"})`,
+        });
+        rt.bridge.emitClientEvent({ type: "system_event", event: "agent_end" });
+      }
+    });
 
     const provider = o.provider ?? this.cfg.defaults.provider;
     const model = o.model ?? this.cfg.defaults.model;