SQL Server 2022

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CREATE TABLE Sale (
    DatePrice DATE,
    Price DECIMAL(9,2)
);

INSERT INTO Sale (DatePrice, Price) VALUES
('2020-05-03', 40.00),
('2020-05-05', NULL),
('2020-05-06', NULL),
('2020-05-07', 30.00),
('2020-05-30', NULL),
('2020-06-01', NULL),
('2020-06-03', NULL),
('2020-06-05', 55.00);

WITH SalesWithMonth AS (
    SELECT
        DatePrice
        , Price
        , MAX(CASE WHEN Price IS NOT NULL THEN DatePrice END) OVER (
            PARTITION BY YEAR(DatePrice), MONTH(DatePrice)
            ORDER BY DatePrice
            ROWS BETWEEN UNBOUNDED PRECEDING AND CURRENT ROW
        ) MaxDatePrice
        , MIN(CASE WHEN Price IS NOT NULL THEN DatePrice END) OVER (
            PARTITION BY YEAR(DatePrice), MONTH(DatePrice)
            ORDER BY DatePrice
            ROWS BETWEEN CURRENT ROW AND UNBOUNDED FOLLOWING
        ) MinDatePrice
    FROM Sale
)
SELECT swm.DatePrice [Date], coalesce(s.Price, swm.Price) Price, s.DatePrice PriceDate
FROM SalesWithMonth swm
LEFT JOIN Sale s ON s.DatePrice = CASE WHEN swm.Price IS NULL THEN COALESCE(MaxDatePrice, MinDatePrice) END
ORDER BY swm.DatePrice;

Date	Price	PriceDate
2020-05-03	40.00	null
2020-05-05	40.00	2020-05-03
2020-05-06	40.00	2020-05-03
2020-05-07	30.00	null
2020-05-30	30.00	2020-05-07
2020-06-01	55.00	2020-06-05
2020-06-03	55.00	2020-06-05
2020-06-05	55.00	null

Warning: Null value is eliminated by an aggregate or other SET operation.