feat(background-agent): integrate file writing in completion path and remove dead council code

- Add _isCompleting guard and writeTaskOutput call before status flip
- Propagate writeOutputToFile from LaunchInput to BackgroundTask
- Delete council-result-format.ts and tests (no longer needed)
- 38/38 tests passing

src/features/background-agent/manager.ts

@@ -80,6 +80,7 @@ import {
   type SubagentSpawnContext,
 } from "./subagent-spawn-limits"
 
+import { writeTaskOutput } from "./task-output-writer"
 type OpencodeClient = PluginInput["client"]
 
 
@@ -1690,6 +1691,16 @@ export class BackgroundManager {
       return false
     }
 
+    // Prevent concurrent re-entry during async file write
+    if (task._isCompleting) return false
+    task._isCompleting = true
+
+    // Write output to file if requested (before status flip)
+    if (task.writeOutputToFile) {
+      const filePath = await writeTaskOutput(task, this.client)
+      if (filePath) task.outputFilePath = filePath
+    }
+
     // Atomically mark as completed to prevent race conditions
     task.status = "completed"
     task.completedAt = new Date()

src/features/background-agent/spawner.ts

@@ -64,6 +64,7 @@ export function createTask(input: LaunchInput): BackgroundTask {
     parentModel: input.parentModel,
     parentAgent: input.parentAgent,
     model: input.model,
+    writeOutputToFile: input.writeOutputToFile,
   }
 }