fix: prevent agents from duplicating delegated subagent work

Ultraworked with [Sisyphus](https://github.com/code-yeongyu/oh-my-openagent)

Co-authored-by: Sisyphus <clio-agent@sisyphuslabs.ai>

src/tools/background-task/create-background-output.ts

@@ -87,7 +87,6 @@ export function createBackgroundOutput(manager: BackgroundOutputManager, client:
 
         const shouldBlock = args.block === true
         const timeoutMs = Math.min(args.timeout ?? 60000, 600000)
-        const fullSession = args.full_session ?? true
 
         let resolvedTask = task
 
@@ -123,6 +122,10 @@ export function createBackgroundOutput(manager: BackgroundOutputManager, client:
         }
 
         const isActive = isTaskActiveStatus(resolvedTask.status)
+        const fullSessionProvided = args.full_session !== undefined
+        const fullSession = fullSessionProvided
+          ? (args.full_session ?? true)
+          : !isActive
         const includeThinking = isActive || (args.include_thinking ?? false)
         const includeToolResults = isActive || (args.include_tool_results ?? false)