Add ToC directly after

Answering my own question, it appears there is no shortcode in this plugin. So changing the aforementioned function is a no go, unforunately.

Luckily, Table of Contents Plus does provide a shortcode, so add to your ‘site specific plugin’:

add_filter( 'the_content', 'saotn_insert_post_toc' );
function saotn_insert_post_toc( $content ) {
    if ( is_single() && !is_admin() && get_post_type() === 'post' ) {
        return saotn_insert_toc_after_first_p( $content );
    }
    return $content;
}
function saotn_insert_toc_after_first_p( $content ) {
    $closing_p = '</p>';
    $paragraphs = explode( $closing_p, $content );
	foreach ($paragraphs as $index => $paragraph) {
		$paragraphs[$index] .= $closing_p;
		if ( in_array($index, array(1)) ) {
			$paragraphs[$index] .= do_shortcode("[toc]");
		}
	}
    return implode( '', $paragraphs );
}

Please re-introduce shortcodes.