fix(background-agent): decrement spawn budget on task completion, cancellation, error, and interrupt

rootDescendantCounts was incremented on every spawn but never decremented
when tasks reached terminal states (completed, cancelled, error, interrupt,
stale-pruned). This made maxDescendants=50 a session-lifetime quota instead
of its intended semantics as a concurrent-active agent cap.

Fix: add unregisterRootDescendant() in five terminal-state handlers:
- tryCompleteTask(): task completes successfully
- cancelTask(): running task cancelled (wasRunning guard prevents
  double-decrement for pending tasks already handled by
  rollbackPreStartDescendantReservation)
- session.error handler: task errors
- promptAsync catch (startTask): task interrupted on launch
- promptAsync catch (resume): task interrupted on resume
- onTaskPruned callback: stale task pruned (wasPending guard)

Fixes: code-yeongyu/oh-my-openagent#2700

src/features/background-agent/manager.ts

@@ -543,6 +543,9 @@ export class BackgroundManager {
           existingTask.error = errorMessage
         }
         existingTask.completedAt = new Date()
+        if (existingTask.rootSessionID) {
+          this.unregisterRootDescendant(existingTask.rootSessionID)
+        }
         if (existingTask.concurrencyKey) {
           this.concurrencyManager.release(existingTask.concurrencyKey)
           existingTask.concurrencyKey = undefined
@@ -813,6 +816,9 @@ export class BackgroundManager {
       const errorMessage = error instanceof Error ? error.message : String(error)
       existingTask.error = errorMessage
       existingTask.completedAt = new Date()
+      if (existingTask.rootSessionID) {
+        this.unregisterRootDescendant(existingTask.rootSessionID)
+      }
 
       // Release concurrency on error to prevent slot leaks
       if (existingTask.concurrencyKey) {
@@ -1009,6 +1015,9 @@ export class BackgroundManager {
       task.status = "error"
       task.error = errorMsg
       task.completedAt = new Date()
+      if (task.rootSessionID) {
+        this.unregisterRootDescendant(task.rootSessionID)
+      }
       this.taskHistory.record(task.parentSessionID, { id: task.id, sessionID: task.sessionID, agent: task.agent, description: task.description, status: "error", category: task.category, startedAt: task.startedAt, completedAt: task.completedAt })
 
       if (task.concurrencyKey) {
@@ -1341,8 +1350,12 @@ export class BackgroundManager {
       log("[background-agent] Cancelled pending task:", { taskId, key })
     }
 
+    const wasRunning = task.status === "running"
     task.status = "cancelled"
     task.completedAt = new Date()
+    if (wasRunning && task.rootSessionID) {
+      this.unregisterRootDescendant(task.rootSessionID)
+    }
     if (reason) {
       task.error = reason
     }
@@ -1463,6 +1476,10 @@ export class BackgroundManager {
     task.completedAt = new Date()
     this.taskHistory.record(task.parentSessionID, { id: task.id, sessionID: task.sessionID, agent: task.agent, description: task.description, status: "completed", category: task.category, startedAt: task.startedAt, completedAt: task.completedAt })
 
+    if (task.rootSessionID) {
+      this.unregisterRootDescendant(task.rootSessionID)
+    }
+
     removeTaskToastTracking(task.id)
 
     // Release concurrency BEFORE any async operations to prevent slot leaks
@@ -1701,6 +1718,9 @@ Use \`background_output(task_id="${task.id}")\` to retrieve this result when rea
         task.status = "error"
         task.error = errorMessage
         task.completedAt = new Date()
+        if (!wasPending && task.rootSessionID) {
+          this.unregisterRootDescendant(task.rootSessionID)
+        }
         this.taskHistory.record(task.parentSessionID, { id: task.id, sessionID: task.sessionID, agent: task.agent, description: task.description, status: "error", category: task.category, startedAt: task.startedAt, completedAt: task.completedAt })
         if (task.concurrencyKey) {
           this.concurrencyManager.release(task.concurrencyKey)