Is there a way to label the results of a GROUP BY GROUPING SETS expression in Snowflake?

So, for example, If we have the following query

WITH data (product, customer, cost) 
AS(
SELECT      * 
FROM        VALUES 
            ('Igloo', 'John', 5000)     ,
            ('Igloo', 'John', 5000)     ,
            ('Donkey', 'John', 1000)    ,
            ('Donkey', 'Jane', 1000)    ,
            ('Mortgage', 'John''s Brother, Jim', 1000)
    )
SELECT      product, 
            customer, 
            SUM(cost) AS sum_cost
FROM        data
GROUP BY    GROUPING SETS ((product), (customer), ())
ORDER BY    GROUPING(product, customer);

I am wondering if Snowflake has a built-in method to generate an indicator column that gives you a guaranteed correct label for which group was used in the grouping sets.

I’d like to know if there is a different/better way to achieve this than using a CASE WHEN clause which won’t necessarily give you a guaranteed correct result in all cases (I think).

Below, is an example of a generated indicator column using a CASE WHEN statement for a simple example.

WITH data (product, customer, cost) 
AS(
SELECT      * 
FROM        VALUES 
            ('Igloo', 'John', 5000)     ,
            ('Igloo', 'John', 5000)     ,
            ('Donkey', 'John', 1000)    ,
            ('Donkey', 'Jane', 1000)    ,
            ('Mortgage', 'John''s Brother, Jim', 1000)
    )
SELECT      product, 
            customer, 
            SUM(cost) AS sum_cost,
            CASE 
                WHEN customer IS NULL AND product  IS NOT NULL THEN 'PRODUCT'
                WHEN product  IS NULL AND customer IS NOT NULL THEN 'CUSTOMER'
                WHEN customer IS NULL AND product  IS NULL     THEN ''
            END AS indicator
FROM        data
GROUP BY    GROUPING SETS ((product), (customer), ())
ORDER BY    GROUPING(product, customer);

If you’d have ten or twenty GROUPING SETS, one can imagine a CASE WHEN statement to not be a desirable/viable solution.

Any help is appreciated.