Sorting search results with custom dropdown

The post date isn’t meta. You only orderby meta_value if the value is a custom field stored in the wp_postmeta table. The publication date is in the wp_posts table and part of the core post data.

If you want to order by date you set orderby to date, and don’t set any of the meta_ vars.

However, setting orderby and order with query strings is supported automatically, without pre_get_posts. For example, if you want to view Make WordPress Core’s posts in reverse alphabetical order, you can just go to https://make.wordpress.org/core/?order=DESC&orderby=title and it’ll work (no posts starting with Z yet!).

So all your function needs to do is handle the property_price2 and area2 orderby values, which WordPress won’t understand on its own.

function wpse_139657_orderby() {    
    if ( isset( $_GET['orderby'] ) ) {
        if ( in_array( $_GET['orderby'], ['property_price2', 'area2'] ) ) {
            set_query_var( 'orderby', 'meta_value_num' );
            set_query_var( 'meta_key', $_GET['orderby'] );
        }
    }
}
add_filter( 'pre_get_posts', 'wpse_139657_orderby' );