Search WordPress Hook for completed Elementor Update

If I understand correctly, you want to do this:

add_action('upgrader_process_complete', 'my_clear_elementor_cache');
function my_clear_elementor_cache()
{
    // Make sure that Elementor loaded and the hook fired
    if (did_action('elementor/loaded')) {
        // Automatically purge and regenerate the Elementor CSS cache
        \Elementor\Plugin::instance()->files_manager->clear_cache();
    }
}