feat: optimize subagent list children query

packages/host/apiproxy/src/api/subagents.schema.ts

@@ -16,6 +16,7 @@ export const subagentListEntrySchema = z.union([
     id: sessionIdSchema,
     mode: z.literal('one-shot'),
     activity: z.union([z.literal('running'), z.literal('inactive')]),
+    hasChildren: z.boolean(),
     label: z.string().optional(),
   }),
   z.object({
@@ -23,6 +24,7 @@ export const subagentListEntrySchema = z.union([
     id: sessionIdSchema,
     mode: z.literal('continuable'),
     activity: z.union([z.literal('running'), z.literal('inactive')]),
+    hasChildren: z.boolean(),
     label: z.string(),
   }),
   z.object({

packages/host/apiproxy/src/api/subagents.ts

@@ -16,6 +16,8 @@ export type SubagentListEntry =
     kind: 'child'
     id: SessionId
     activity: 'running' | 'inactive'
+    /** Whether a direct descendant has durable `origin: 'subagent'`. */
+    hasChildren: boolean
   } & (
     | {
       mode: 'one-shot'