fix(agent-loop): order admission publication and gate idle on committed turns

Three ordering fixes on the admission and settlement boundaries.

kick() installs the abort owner, marks the interval busy (running is
emitted before any listener can observe the claim), and installs the
pending done BEFORE publishing agent/inbox/dequeue: a dequeue listener
that cancels or disposes now finds live cancellation and quiescence
ownership instead of the previous activity's settled state, and claimed
prompt admission — including asynchronous prompt-submit hooks — sits
inside the running interval where cancel routing can reach it. The
admission-rejected path yields one microtask before continueOrIdle so
the idle transition cannot fire inside send()'s synchronous extent.

agent/idle now names only committed turns: a run that aborts or fails
before its turn/start commits exits without the notification, since
there is no durable turn/end for settlement consumers to act against.
The event's JSDoc states the narrowed contract.

packages/core/agent-loop/src/agent.ts

@@ -201,9 +201,18 @@ export class ReactLoopAgent implements Agent {
     // eslint-disable-next-line @typescript-eslint/no-non-null-assertion
     const { message } = this.queued.shift()!
 
-    emitAgentEvent(this.loopCtx, this, 'agent/inbox/dequeue', message)
     const admission = new AbortController()
     this.abort = admission
+    // Claimed admission is part of the running interval: it is cancellable
+    // activity, so observers (and their cancel routing) must see it.
+    if (!this.busy) {
+      this.busy = true
+      emitAgentEvent(this.loopCtx, this, 'agent/status', 'running')
+    }
+    // The admission body runs synchronously up to the prompt-submit
+    // waterfall's first await, so the waterfall snapshots its listeners
+    // before a disposal initiated by the running-status emit above can
+    // unregister a vetoing plugin.
     this.done = this.loopCtx.agents.withInitiator(this, async () => {
       const signal = admission.signal
       const trigger: TurnTrigger = { kind: 'message', source: message.source }
@@ -235,11 +244,19 @@ export class ReactLoopAgent implements Agent {
       // still owns the slot here and releasing it unconditionally is exact.
       this.abort = undefined
       if (admitted === undefined) {
+        // A synchronously aborted admission would otherwise publish idle
+        // inside send()'s own synchronous extent, before any post-send
+        // subscriber could observe the transition.
+        await Promise.resolve()
         this.continueOrIdle()
         return
       }
       await this.run(trigger, admitted)
     })
+    // Published only after the abort owner and pending done are installed: a
+    // dequeue listener that cancels or disposes must find live cancellation
+    // and quiescence ownership, not the previous activity's settled state.
+    emitAgentEvent(this.loopCtx, this, 'agent/inbox/dequeue', message)
   }
 
   /**
@@ -260,6 +277,7 @@ export class ReactLoopAgent implements Agent {
     const signal = controller.signal
     const turn = this.lastTurn + 1
     let step = 0
+    let opened = false
     let reason: TurnEndReason = { kind: 'completed' }
     let idle: IdleReason = { kind: 'completed' }
     let retry = false
@@ -272,6 +290,7 @@ export class ReactLoopAgent implements Agent {
       // Committed: publish the turn to the machine's own bookkeeping and let
       // the admitted input enter the log it now belongs to.
       this.turnOpen = true
+      opened = true
       this.lastTurn = turn
       for (const input of admitted) {
         this.session.append('user/message', input, { surfaceOp: 'append' })
@@ -368,7 +387,10 @@ export class ReactLoopAgent implements Agent {
     if (retry) {
       await this.run({ kind: 'retry' })
     } else {
-      emitAgentEvent(this.loopCtx, this, 'agent/idle', turn, idle)
+      // agent/idle names only committed turns: a run aborted or rejected
+      // before turn/start has no durable turn/end for consumers to settle
+      // against, so it exits without the notification.
+      if (opened) emitAgentEvent(this.loopCtx, this, 'agent/idle', turn, idle)
       this.continueOrIdle()
     }
   }
@@ -592,7 +614,9 @@ export class ReactLoopAgent implements Agent {
     if (this.abort !== undefined) return
     if (this.queued.some(item => item.wakeup)) {
       this.kick()
-    } else if (this.busy) {
+    } else {
+      // Every caller sits inside an admission or run whose install marked the
+      // interval busy, so the flag is still set here.
       this.busy = false
       emitAgentEvent(this.loopCtx, this, 'agent/status', 'idle')
     }