How Can I Have A URL Changed Based on the Originating URL?

You can use the page_link filter with the same logic as the page_template filter in the other answer. If the endpoint query var is set, then any link to a page gets the app-view/ appended:

function wpd_page_link( $link, $post_id ){
    global $wp_query;
    if( isset( $wp_query->query_vars['app-view'] ) ){
        return $link . 'app-view/';
    }
    return $link;
}
add_filter( 'page_link', 'wpd_page_link', 10, 2 );