fix(site): scope chevron to icon hover when any child is running (#22456)

Follow-up to #22452. The previous fix only checked the chat's own
status, so a root chat in `waiting` status with actively running
sub-agents still showed the expand/collapse chevron on full-row hover.

## Problem

A root chat that's idle (`waiting`/`completed`) but has running
sub-agents would still swap its status icon for the `>` chevron on row
hover. The fix in #22452 only gated on `chat.status` being
`pending`/`running`, which doesn't cover the parent when sub-agents are
the ones executing.

## Fix

`isExecuting` now also checks whether **any direct child** is
`pending`/`running`:

```ts
const isExecuting =
  chat.status === "pending" ||
  chat.status === "running" ||
  (hasChildren &&
    childIDs.some((id) => {
      const c = chatById.get(id);
      return c?.status === "pending" || c?.status === "running";
    }));
```

When `isExecuting` is true, the chevron only appears on hover of the
icon area itself (`group-hover/icon`), not the entire row.

## New story

Added `IdleParentWithRunningChild` — verifies a `waiting` parent with a
`running` child uses icon-only hover scope for the toggle.

Co-authored-by: Coder <coder@users.noreply.github.com>

site/src/pages/AgentsPage/AgentsSidebar.stories.tsx

@@ -240,6 +240,46 @@ export const RunningChatPreservesSpinner: Story = {
 	},
 };
 
+// When a root chat is idle but has a running child, the chevron
+// should still be scoped to the icon area hover, not the full row.
+export const IdleParentWithRunningChild: Story = {
+	args: {
+		chats: [
+			buildChat({
+				id: "idle-parent",
+				title: "Idle parent agent",
+				status: "waiting",
+			}),
+			buildChat({
+				id: "running-child",
+				title: "Running sub-agent",
+				status: "running",
+				parent_chat_id: "idle-parent",
+				root_chat_id: "idle-parent",
+			}),
+		],
+	},
+	parameters: {
+		reactRouter: reactRouterParameters({
+			location: {
+				path: "/agents/running-child",
+				pathParams: { agentId: "running-child" },
+			},
+			routing: agentsRouting,
+		}),
+	},
+	play: async ({ canvasElement }) => {
+		const canvas = within(canvasElement);
+
+		// The parent's toggle should use icon-only hover scope because
+		// its child is actively running.
+		const toggle = canvas.getByTestId("agents-tree-toggle-idle-parent");
+		await expect(toggle).toBeInTheDocument();
+		await expect(toggle.className).toMatch(/\binvisible\b/);
+		await expect(toggle.className).toContain("group-hover/icon:visible");
+	},
+};
+
 export const ActiveChatAncestryExpanded: Story = {
 	args: {
 		chats: [

site/src/pages/AgentsPage/AgentsSidebar.tsx

@@ -327,7 +327,14 @@ const ChatTreeNode = memo<ChatTreeNodeProps>(({ chat, isChildNode }) => {
 	}`;
 	const isArchivingThisChat = isArchiving && archivingChatId === chat.id;
 	const isExpanded = normalizedSearch ? true : (expandedById[chatID] ?? false);
-	const isExecuting = chat.status === "pending" || chat.status === "running";
+	const isExecuting =
+		chat.status === "pending" ||
+		chat.status === "running" ||
+		(hasChildren &&
+			childIDs.some((id) => {
+				const c = chatById.get(id);
+				return c?.status === "pending" || c?.status === "running";
+			}));
 
 	return (
 		<div className="flex min-w-0 flex-col">