Function run_background_task 

pub async fn run_background_task(
    task: &str,
    provider: Arc<dyn LlmProvider>,
    tools: Arc<ToolRegistry>,
    context: ToolContext,
    config: Config,
    ctx: Arc<dyn CtxBuilder>,
    _progress_tx: UnboundedSender<AgentEvent>,
) -> AgentEvent

Run a background task with an independent conversation and turn runner. Sends progress events through progress_tx so the TUI can show updates.