SQL Server 2019

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WITH yourTable AS (
    SELECT 'Bay' AS store, '2022-01-01' AS date, 'true' AS is_open UNION ALL
    SELECT 'Bay', '2022-02-01', 'true' UNION ALL
    SELECT 'Bay', '2022-03-01', 'true' UNION ALL
    SELECT 'Bay', '2022-04-01', 'false' UNION ALL
    SELECT 'Bay', '2022-05-01', 'false' UNION ALL
    SELECT 'Bay', '2022-06-01', 'false' UNION ALL
    SELECT 'Bay', '2022-07-01', 'true' UNION ALL
    SELECT 'Bay', '2022-08-01', 'true' UNION ALL
    SELECT 'Bay', '2022-09-01', 'true' UNION ALL
    SELECT 'Walmart', '2022-07-01', 'true' UNION ALL
    SELECT 'Walmart', '2022-08-01', 'false' UNION ALL
    SELECT 'Walmart', '2022-09-01', 'true'
),
cte AS (
    SELECT t.*, ROW_NUMBER() OVER (PARTITION BY store ORDER BY date) rn1,
                ROW_NUMBER() OVER (PARTITION BY store, is_open ORDER BY date) rn2
    FROM yourTable t
),
cte2 AS (
    SELECT t.*, MIN(date) OVER (PARTITION BY store, is_open, rn1 - rn2) AS min_date
    FROM cte t
)

SELECT store, date, is_open,
       DENSE_RANK() OVER (PARTITION BY store ORDER BY rn1 - rn2, min_date) "group"
FROM cte2
ORDER BY store, date;

store	date	is_open	group
Bay	2022-01-01	true	1
Bay	2022-02-01	true	1
Bay	2022-03-01	true	1
Bay	2022-04-01	false	2
Bay	2022-05-01	false	2
Bay	2022-06-01	false	2
Bay	2022-07-01	true	3
Bay	2022-08-01	true	3
Bay	2022-09-01	true	3
Walmart	2022-07-01	true	1
Walmart	2022-08-01	false	2
Walmart	2022-09-01	true	3