Restrict Media Library so users only see own media

There are no settings within Access to limit who can see what content in the Media Library.

You can use the WordPress filter ‘ajax_query_attachments_args’ to add restrictions, such as to only show a user their own media, like so:

add_filter( 'ajax_query_attachments_args', 'show_current_user_attachments', 10, 1 );
function show_current_user_attachments( $query = array() ) {

    $user_id = get_current_user_id();
    if( $user_id ) {
        $query['author'] = $user_id;
    }
    return $query;
}

From https://codex.wordpress.org/Plugin_API/Filter_Reference/ajax_query_attachments_args#Examples