Рабочий вариант:

Возможно ssl сертификат и не нужен, но я поставил Lets encrypt.

MAIL_DRIVER=smtp
MAIL_HOST=smtp.mail.ru
MAIL_PORT=465
MAIL_USERNAME=domen.zone@mail.ru
MAIL_PASSWORD=pass
MAIL_ENCRYPTION=ssl
MAIL_FROM_ADDRESS=domen.zone@mail.ru
MAIL_FROM_NAME='tra ta ta'

await page.waitForSelector('.textdivresp').then(() => {
        console.log('textdivresp_ololo');
    });

    await page.evaluate(() => {
        let elements = document.getElementsByClassName('textdivresp');
        elements[1].click()
    });

В модели Departments добавил метод - примерно то, что мне надо:

public static function  getProviderByTotalParams()
    {
        $mainTable = self::tableName();

        $sql = '
             SELECT m_departments.id, m_departments.name, 
             COUNT(m_news.id) + COUNT(m_posts.id) + COUNT(m_forums.id) + COUNT(m_questions.id) AS total_count
            FROM m_departments 
            LEFT JOIN m_news ON m_departments.id = m_news.department_id
            LEFT JOIN m_posts ON m_departments.id = m_posts.department_id
            
            GROUP BY m_departments.id
            ORDER BY total_count DESC
            LIMIT 5
        ';

        $dataProvider = new SqlDataProvider([
            'sql' => $sql, 
            'totalCount' => 5, 
            'pagination' => [
                'pageSize' => 5, 
            ],
        ]);;

        return $dataProvider;
    }