Display all post titles of current post type

As you are on, ‘single-press.php’ , this is single ‘press’ post type page. As per your question, it seems you want to display archive of all ‘press’ posts, along with current posts highlighted.

As we are on single ‘press’ post page, no need to check for post type.

We can directly add following loop with modification in structure, as per your need,

global $post;
$post_args = array(
        'post_type' => 'press',
        'post_status' => 'publish'
        );
$press_posts = get_posts($post_args);   
if(!empty($press_posts)){
foreach($pres_posts as $single_post){
    ?>
    <a href="https://wordpress.stackexchange.com/questions/162905/<?php echo get_permalink($post_id); ?>" class="<?php if($single_post->ID == $post->ID ) echo 'wdm-current-post'; ?>"><?php echo $single_post->post_title; ?></a><?php
}
}

So now we have given a class ‘wdm-current-post’ to the current post. All the posts will now be listed with the current post highlighted in the list.