Function tear_off_pool_promote 

pub fn tear_off_pool_promote(
    state: &Arc<AppState>,
    args: &Value,
) -> Result<Value, String>

Phase 6 — promote a pre-warmed pool window for tear-off. Returns the promoted window’s label, or an error string if the pool was empty (caller should fall back to open_window_at_position). Args: { workspaceId, screenX, screenY }.