Receive each week the number of posts published

Question

Here is a basic use for WP_Query that returns an object containing all posts for the current week as $query. The last line echos the property `found_posts’, which provides the count for the week query.

    $args = array(
        'date_query' => array(
            array(
                'year' => date( 'Y' ),
                'week' => date( 'W' ),
            ),
        ),
    );
    $query = new WP_Query( $args );
    echo $query->found_posts;

For your purposes, I do not know if the week is based on an empirical calendar or if this is based on your site’s Settings > General > date settings.

With a little testing you should be able to produce reliable results for your email each week. https://codex.wordpress.org/Class_Reference/WP_Query#Date_Parameters