Need to update Publisher_channel_categories.php with the changes in EE4. Create a Publisher_channel_categories_ee4.php version and load it conditionally in the following methods.

public function channel_module_categories_start()
    {
        ee()->load->library('Publisher_channel_categories');
        return ee()->publisher_channel_categories->categories();
    }

    /**
     * @return string
     */
    public function channel_module_category_heading_start()
    {
        ee()->load->library('Publisher_channel_categories');
        return ee()->publisher_channel_categories->category_heading();
    }