feat(background-agent): restrict tool access in subagent execution to prevent recursive calls

- Disable 'task' and 'call_omo_agent' tools in BackgroundManager
- Disable recursive background operation tools in call_omo_agent sync execution
- Prevents agents from spawning background tasks or calling themselves

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Author: code-yeongyu

src/features/background-agent/manager.ts

@@ -82,10 +82,8 @@ export class BackgroundManager {
       body: {
         agent: input.agent,
         tools: {
+          task: false,
           background_task: false,
-          background_output: false,
-          background_cancel: false,
-          call_omo_agent: false,
         },
         parts: [{ type: "text", text: input.prompt }],
       },

src/tools/call-omo-agent/tools.ts

@@ -123,6 +123,9 @@ async function executeSync(
         tools: {
           task: false,
           call_omo_agent: false,
+          background_task: false,
+          background_output: false,
+          background_cancel: false,
         },
         parts: [{ type: "text", text: args.prompt }],
       },