Active language always displayed as the first language

Would MslsOutput do what you need? https://msls.co/functions-classes-and-methods/

Probably, but I’m not sure how I should change the order using this function.

Something like this might be OK?

$object   = new MslsOutput();
$display  = 0;
$exists   = false;
$links    = $object->get( $display, $exists );
$filtered = array();
foreach ( $links as $link ) {
    if ( FALSE === strpos( 'current_language', $link ) ) {
        $filtered[] = $link;
    }
    else {
        echo $link;
    }
}
echo implode( '', $filtered );