You can try this filter:
function custom_theme_titles( $titleparts ) {
$pagetitle = $titleparts['title'];
$date = date('l jS F Y');
$sep = " | ";
$titleparts['title'] = $pagetitle.$sep.$date;
unset( $titleparts['site'] );
return $titleparts;
}
add_filter( 'document_title_parts', 'custom_theme_titles', PHP_INT_MAX );
Just to let you know Yoast used to include currentDate variables in there meta editor – there now deprecated and they advise against this practice.