public function actionTest()
{
    $begin = new DateTime('2021-01-01');
    $end = new DateTime('2023-01-01');

    $interval = DateInterval::createFromDateString('1 day');
    $period = new DatePeriod($begin, $interval, $end);

    foreach ($period as $dt) {
        $date = $dt->format('Y-m-d');
        $res = $this->makeSql($date);
        echo $date . ': ' . $res['q'] . ' (' . $res['ids'] . ')' .  PHP_EOL;
    }
}

/**
 * @param $date
 * @return array
 * @throws \yii\db\Exception
 */
private function makeSql($date): array
{
    $sql = 'SELECT COUNT(id) AS q
                 , GROUP_CONCAT(id) AS ids
            FROM yii_doc.season_char_settings
            WHERE (
                      start_day_month_date
                      + INTERVAL YEAR(:DATE)
                      - IF(MONTH(finish_day_month_date) < MONTH(start_day_month_date) AND MONTH(:DATE) < 6, 1, 0) YEAR
                  ) <= :DATE
              AND :DATE < (
                    finish_day_month_date
                    + INTERVAL YEAR(:DATE)
                    + IF(MONTH(finish_day_month_date) < MONTH(start_day_month_date) AND MONTH(:DATE) > 6, 1, 0) YEAR
                )';

    return Yii::$app->db
        ->createCommand($sql, [':DATE' => $date])
        ->queryOne();
}