MySQL 8.0

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CREATE TABLE YourTable
(DATE_SERV date)
;
    
INSERT INTO YourTable ( DATE_SERV )
VALUES
    ('2022-01-01'),
    ('2022-01-02'),
    ('2022-01-03'),
    ('2022-01-05'),
    ('2022-01-06'),
    ('2022-01-09'),
    ('2022-01-10'),
    ('2022-01-11')
;

Records: 8  Duplicates: 0  Warnings: 0


SELECT DATE_SERV
       , LAG(DATE_SERV,1) OVER (ORDER BY DATE_SERV) AS Prev_Date
FROM   YourTable


DATE_SERV
Prev_Date


2022-01-01
null

2022-01-02
2022-01-01

2022-01-03
2022-01-02

2022-01-05
2022-01-03

2022-01-06
2022-01-05

2022-01-09
2022-01-06

2022-01-10
2022-01-09

2022-01-11
2022-01-10


SELECT
        DATE_SERV
        , SUM( IF( DATEDIFF(DATE_SERV, Prev_Date) = 1, 0, 1) ) OVER(
                   ORDER BY DATE_SERV 
        )  AS DateGroup_Num
FROM
      (
         SELECT DATE_SERV
                , LAG(DATE_SERV,1) OVER (
                       ORDER BY DATE_SERV
                ) AS Prev_Date
         FROM   YourTable
      ) grp


DATE_SERV
DateGroup_Num


2022-01-01
1

2022-01-02
1

2022-01-03
1

2022-01-05
2

2022-01-06
2

2022-01-09
3

2022-01-10
3

2022-01-11
3


SELECT 
       t.DATE_SERV
       , DATEDIFF( 
            t.DATE_SERV
            , MIN(t.DATE_SERV) OVER( 
                  PARTITION BY t.DateGroup_Num 
                  ORDER BY t.DATE_SERV 
             )
        ) +1 AS Consecutive_Days
FROM ( 
        SELECT
               DATE_SERV
              , SUM( IF( DATEDIFF(DATE_SERV, Prev_Date) = 1, 0, 1) ) OVER(
                    ORDER BY DATE_SERV 
                )  AS DateGroup_Num
        FROM
        (
                SELECT DATE_SERV
                       , LAG(DATE_SERV,1) OVER (
                            ORDER BY DATE_SERV
                         ) AS Prev_Date
                FROM   YourTable
        ) grp
    ) t


DATE_SERV
Consecutive_Days


2022-01-01
1

2022-01-02
2

2022-01-03
3

2022-01-05
1

2022-01-06
2

2022-01-09
1

2022-01-10
2

2022-01-11
3

DATE_SERV	Prev_Date
2022-01-01	null
2022-01-02	2022-01-01
2022-01-03	2022-01-02
2022-01-05	2022-01-03
2022-01-06	2022-01-05
2022-01-09	2022-01-06
2022-01-10	2022-01-09
2022-01-11	2022-01-10