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You must execute the code again to save those values in the database.

DROP TABLE IF EXISTS #Price
CREATE TABLE #Price (DataId INT IDENTITY(1,1), NameOfWidget VARCHAR(50), Price MONEY, PriceScheduleId INT, StartEffectiveWhen DATE, EndEffectiveWhen DATE)

INSERT INTO #Price (NameOfWidget, Price, PriceScheduleId, StartEffectiveWhen, EndEffectiveWhen)
VALUES
    ('CoolWidget', 3.51, 1, '2015-1-1', '2021-12-31'),
    ('CoolWidget', 2.00, 2, '2017-1-1', '2022-12-31'),
    ('CoolWidget', 4.23, 1, '2021-1-1', '2100-12-31'),
    ('CoolWidget', 2.00, 2, '2021-1-1', '2100-12-31'),
    ('OtherWidget', 13.24, 1, '2014-1-1', '2018-5-4'),
    ('OtherWidget', 13.24, 1, '2018-5-6', '2019-12-31'),
    ('OtherWidget', 13.24, 1, '2020-1-1', '2100-12-31')

;WITH OrderedDates AS 
(
    SELECT  priceStart.NameOfWidget, priceStart.StartEffectiveWhen AS DateWhen, 1 AS IsStartDate, 0 AS IsEndDate
    FROM    #Price priceStart

UNION

SELECT  priceStart.NameOfWidget, priceStart.EndEffectiveWhen AS DateWhen, 0 AS IsStartDate, 1 AS IsEndDate
    FROM    #Price priceStart
    
)
SELECT  OrderedDates.NameOfWidget,
        CASE 
            WHEN LAG(OrderedDates.DateWhen) OVER (PARTITION BY OrderedDates.NameOfWidget ORDER BY OrderedDates.DateWhen) IS NULL THEN '1900-1-1'
            WHEN LAG(OrderedDates.IsStartDate ) OVER (PARTITION BY OrderedDates.NameOfWidget ORDER BY OrderedDates.DateWhen) = 1 
                THEN  LAG(OrderedDates.DateWhen) OVER (PARTITION BY OrderedDates.NameOfWidget ORDER BY OrderedDates.DateWhen)
            ELSE DATEADD(DAY, 1, LAG(OrderedDates.DateWhen) OVER (PARTITION BY OrderedDates.NameOfWidget ORDER BY OrderedDates.DateWhen))
        END AS StartEffectiveWhen, 
        
        CASE
            WHEN OrderedDates.IsEndDate = 1 THEN OrderedDates.DateWhen
            ELSE DATEADD(DAY, -1, OrderedDates.DateWhen)
        END AS EndEffectiveWhen
FROM    OrderedDates
ORDER BY OrderedDates.NameOfWidget

NameOfWidget	StartEffectiveWhen	EndEffectiveWhen
CoolWidget	1900-01-01	2014-12-31
CoolWidget	2015-01-01	2016-12-31
CoolWidget	2017-01-01	2020-12-31
CoolWidget	2021-01-01	2021-12-31
CoolWidget	2022-01-01	2022-12-31
CoolWidget	2023-01-01	2100-12-31
OtherWidget	1900-01-01	2013-12-31
OtherWidget	2014-01-01	2018-05-04
OtherWidget	2018-05-05	2018-05-05
OtherWidget	2018-05-06	2019-12-31
OtherWidget	2020-01-01	2019-12-31
OtherWidget	2020-01-01	2100-12-31

(7 rows affected)

(12 rows affected)