SQL Server 2019

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DECLARE @Data TABLE (Id INT IDENTITY(1,1), Person VARCHAR(100), Date DATETIME, Expected INT, Actual INT)
INSERT @Data (Person, Date, Expected)
VALUES
	('JACK', '2021-01-02', 1),
	('JACK', '2021-01-21', 1),
	('JACK', '2021-01-25', 1),
	('JACK', '2021-02-01', 1),
	('JACK', '2021-02-04', 2),
	('JACK', '2021-02-21', 2),
	('JACK', '2021-03-01', 2),
	('JACK', '2021-03-12', 3),
	('JACK', '2021-03-30', 3),
	('JACK', '2021-04-10', 3),
	('JACK', '2021-04-16', 4),
	('JILL', '2021-01-20', 1),
	('JILL', '2021-01-22', 1),
	('JILL', '2021-01-26', 1),
	('JILL', '2021-02-18', 1),
	('JILL', '2021-02-23', 2),
	('JILL', '2021-02-28', 2),
	('JILL', '2021-03-08', 2),
	('JILL', '2021-03-26', 3),
	('JILL', '2021-03-30', 3),
	('JILL', '2021-04-20', 3),
	('JILL', '2021-04-30', 4)

DECLARE @Id INT
DECLARE @Person VARCHAR(100)
DECLARE @Date DATETIME
DECLARE @PriorPerson VARCHAR(100) = NULL
DECLARE @PriorDate DATETIME = NULL
DECLARE @GroupNumber INT

DECLARE Csr CURSOR FOR 
    SELECT Id, Person, Date
    FROM @Data
    ORDER BY Person, Date
OPEN Csr

FETCH NEXT FROM Csr INTO @Id, @Person, @Date
WHILE @@FETCH_STATUS = 0
BEGIN
    IF @PriorPerson IS NULL OR @Person <> @PriorPerson
	BEGIN
        SET @GroupNumber = 1
        SET @PriorPerson = @Person
        SET @PriorDate = @Date
    END
    ELSE IF @Date >= DATEADD(DAY, 31, @PriorDate)
	BEGIN
        SET @GroupNumber = @GroupNumber + 1
        SET @PriorDate = @Date
    END
    UPDATE @Data SET Actual = @GroupNumber WHERE Id = @Id

FETCH NEXT FROM Csr INTO @Id, @Person, @Date
END

CLOSE Csr
DEALLOCATE Csr

SELECT *, Test = CASE WHEN Expected = Actual THEN 'Match' ELSE 'Mismatch' END
FROM @Data
ORDER BY ID

Id	Person	Date	Expected	Actual	Test
1	JACK	2021-01-02 00:00:00.000	1	1	Match
2	JACK	2021-01-21 00:00:00.000	1	1	Match
3	JACK	2021-01-25 00:00:00.000	1	1	Match
4	JACK	2021-02-01 00:00:00.000	1	1	Match
5	JACK	2021-02-04 00:00:00.000	2	2	Match
6	JACK	2021-02-21 00:00:00.000	2	2	Match
7	JACK	2021-03-01 00:00:00.000	2	2	Match
8	JACK	2021-03-12 00:00:00.000	3	3	Match
9	JACK	2021-03-30 00:00:00.000	3	3	Match
10	JACK	2021-04-10 00:00:00.000	3	3	Match
11	JACK	2021-04-16 00:00:00.000	4	4	Match
12	JILL	2021-01-20 00:00:00.000	1	1	Match
13	JILL	2021-01-22 00:00:00.000	1	1	Match
14	JILL	2021-01-26 00:00:00.000	1	1	Match
15	JILL	2021-02-18 00:00:00.000	1	1	Match
16	JILL	2021-02-23 00:00:00.000	2	2	Match
17	JILL	2021-02-28 00:00:00.000	2	2	Match
18	JILL	2021-03-08 00:00:00.000	2	2	Match
19	JILL	2021-03-26 00:00:00.000	3	3	Match
20	JILL	2021-03-30 00:00:00.000	3	3	Match
21	JILL	2021-04-20 00:00:00.000	3	3	Match
22	JILL	2021-04-30 00:00:00.000	4	4	Match