Cairn

Нельзя группировать просто по номеру месяца в данной ситуации, т.к. у месяцев в разных годах совпадёт номер и они сгруппируются, хотя по идее не должны.

SELECT ID_client, Avg_check, Total_sum, Purchases, ROUND(Total_sum/Purchases,2) AS Avg_transaction
FROM (
  WITH per_check_t AS (
    SELECT 
      FIRST(CONCAT(YEAR(date_new),"-",MONTH(date_new))) AS Month, 
      FIRST(CAST(date_new AS DATE)) AS Date, 
      Id_check, 
      FIRST(ID_client) AS ID_client, 
      ROUND(SUM(Sum_payment),2) AS Check_sum,
      COUNT(*) AS n_transactions
    FROM transactions
    GROUP BY Id_check)
  SELECT 
    ID_client, 
    COUNT(DISTINCT Month) AS Months,
    ROUND(AVG(Check_sum),2) AS Avg_check,
    ROUND(SUM(Check_sum),2) AS Total_sum,
    SUM(n_transactions) AS Purchases
  FROM per_check_t
  GROUP BY per_check_t.ID_client
  HAVING Months = 13
  ORDER BY Total_sum DESC) AS full_months