Function execute 

pub async fn execute(
    tool_name: &str,
    arguments: &str,
    bg_agents: &Arc<BgAgentRegistry>,
    bg_processes: &BgRegistry,
    caller_spawner: Option<u32>,
) -> ToolResult

Dispatch a Layer-2 tool call. Returns a ToolResult in the same shape as ToolRegistry::execute() so the dispatch layer can plug it in without special-casing further.

tool_name must be one of "ListBackgroundTasks", "CancelTask", "WaitTask". Any other name is a programmer error in the dispatch router — we return an err so it’s loud-but-safe in production.