Admin notice on wp_insert_post

Hooks cannot be added directly inside functions. Using do_action, you can invoke a custom hook.

In your case try out the below solution:

add_action( 'wp_insert_post', 'automate_intercom', 10, 3 );
function automate_intercom( $post_id, $post, $update ) {

    if ( $post->post_status == 'publish' && $post->post_type == 'help-center' ) {

        $someCondition = '';

        if ( $someCondition !== '' ) {

        } else {
            show_example_error();
        }
    }
}

function show_example_error() {
    $screen = get_current_screen();
    if ( $screen->post_type == 'help-center' ) {
        $class="notice notice-info";
        $message = __( 'Example error', 'admin_notice' );
        error_log( 'In admin notice ' );
        printf( '<div class="%1$s"><p>%2$s</p></div>', esc_attr( $class ), $message );
    }
}
add_action( 'admin_notices', 'show_example_error' );