fix(desktop): make Agents indicator match the Spawn-tree panel

The status-bar "Agents" item conflated three unrelated signals — running
subagents (aggregated across all sessions), in-flight session turns, and
failed background *system* actions (gateway restarts, toolset installs,
computer-use grants via $desktopActionTasks/preview restart) — yet
clicking it opens AgentsView, which renders only subagents. A failed
gateway restart therefore showed "Agents (1 Failed)" over an empty
"No live subagents" tree. AgentsView also filtered to the active session,
so a subagent running in a background session showed "Agents N running"
with nothing in the tree (the desync reported in #49808).

Unify the scope both surfaces speak:
- AgentsView aggregates subagents across every session (salvages #49819).
- The indicator's running/failed counts come from subagents only
  (aggregated), never background system actions — those keep their own
  surfaces in settings / command center.

So "Agents (N …)" now always points at a populated Spawn tree.

Supersedes #49819. Fixes #49808.

apps/desktop/src/app/shell/hooks/use-statusbar-items.tsx

@@ -22,8 +22,6 @@ import type { RuntimeReadinessResult } from '@/lib/runtime-readiness'
 import { contextBarLabel, LiveDuration, usageContextLabel } from '@/lib/statusbar'
 import { cn } from '@/lib/utils'
 import { setGlobalYolo, setSessionYolo } from '@/lib/yolo-session'
-import { $desktopActionTasks } from '@/store/activity'
-import { $previewServerRestartStatus } from '@/store/preview'
 import {
   $activeSessionId,
   $busy,
@@ -31,11 +29,10 @@ import {
   $currentUsage,
   $sessionStartedAt,
   $turnStartedAt,
-  $workingSessionIds,
   $yoloActive,
   setYoloActive
 } from '@/store/session'
-import { $subagentsBySession, activeSubagentCount } from '@/store/subagents'
+import { $subagentsBySession, activeSubagentCount, failedSubagentCount } from '@/store/subagents'
 import { $gatewayRestarting } from '@/store/system-actions'
 import {
   $backendUpdateApply,
@@ -90,12 +87,9 @@ export function useStatusbarItems({
   const yoloActive = useStore($yoloActive)
   const busy = useStore($busy)
   const currentUsage = useStore($currentUsage)
-  const desktopActionTasks = useStore($desktopActionTasks)
   const gatewayRestarting = useStore($gatewayRestarting)
-  const previewServerRestartStatus = useStore($previewServerRestartStatus)
   const sessionStartedAt = useStore($sessionStartedAt)
   const turnStartedAt = useStore($turnStartedAt)
-  const workingSessionIds = useStore($workingSessionIds)
   const subagentsBySession = useStore($subagentsBySession)
   const updateStatus = useStore($updateStatus)
   const updateApply = useStore($updateApply)
@@ -159,24 +153,17 @@ export function useStatusbarItems({
     [gatewayLogLines, gatewayState, inferenceStatus, openCommandCenterSection, statusSnapshot]
   )
 
-  const { bgFailed, bgRunning, subagentsRunning } = useMemo(() => {
-    const actions = Object.values(desktopActionTasks)
-    const running = actions.filter(t => t.status.running).length
-    const failed = actions.filter(t => !t.status.running && (t.status.exit_code ?? 0) !== 0).length
-    const previewRunning = previewServerRestartStatus === 'running' ? 1 : 0
-    const previewFailed = previewServerRestartStatus === 'error' ? 1 : 0
-
-    const subagentsRunning = Object.values(subagentsBySession).reduce(
-      (sum, items) => sum + activeSubagentCount(items),
-      0
-    )
+  // The indicator must speak the same scope as the Spawn-tree panel it opens:
+  // every session's subagents, never background system actions (gateway
+  // restarts, toolset installs) which surface in their own panels.
+  const { subagentsFailed, subagentsRunning } = useMemo(() => {
+    const lists = Object.values(subagentsBySession)
 
     return {
-      bgFailed: failed + previewFailed,
-      bgRunning: workingSessionIds.length + running + previewRunning,
-      subagentsRunning
+      subagentsFailed: lists.reduce((sum, items) => sum + failedSubagentCount(items), 0),
+      subagentsRunning: lists.reduce((sum, items) => sum + activeSubagentCount(items), 0)
     }
-  }, [desktopActionTasks, previewServerRestartStatus, subagentsBySession, workingSessionIds])
+  }, [subagentsBySession])
 
   const gatewayOpen = gatewayState === 'open'
   const gatewayConnecting = gatewayState === 'connecting'
@@ -321,20 +308,18 @@ export function useStatusbarItems({
       {
         className: cn(
           agentsOpen && 'bg-accent/55 text-foreground',
-          bgFailed > 0 && 'text-destructive hover:text-destructive'
+          subagentsFailed > 0 && 'text-destructive hover:text-destructive'
         ),
         detail:
           subagentsRunning > 0
             ? copy.subagents(subagentsRunning)
-            : bgFailed > 0
-              ? copy.failed(bgFailed)
-              : bgRunning > 0
-                ? copy.running(bgRunning)
-                : undefined,
+            : subagentsFailed > 0
+              ? copy.failed(subagentsFailed)
+              : undefined,
         icon:
-          bgFailed > 0 ? (
+          subagentsFailed > 0 ? (
             <AlertCircle className="size-3" />
-          ) : bgRunning > 0 || subagentsRunning > 0 ? (
+          ) : subagentsRunning > 0 ? (
             <Loader2 className="size-3 animate-spin" />
           ) : (
             <Sparkles className="size-3" />
@@ -356,8 +341,6 @@ export function useStatusbarItems({
     ],
     [
       agentsOpen,
-      bgFailed,
-      bgRunning,
       commandCenterOpen,
       copy,
       gatewayMenuContent,
@@ -367,6 +350,7 @@ export function useStatusbarItems({
       inferenceReady,
       inferenceStatus?.reason,
       openAgents,
+      subagentsFailed,
       subagentsRunning,
       toggleCommandCenter
     ]