Sort values of the columns from largest to smallest in an array and save each ordered value in a new variable

Although I do not know in depth MySQL I understand that what you are looking for is not easy to solve from SQL. No doubt this is a task that you should leave in the hands of the "front-end". Even so, if you must solve it from the database, what I can think of to do is the following:

Basically at a conceptual level, now I present a simple example, which you should adapt to your data structure, it is essential that you have a ID per row, it can be an existing one or eventually you should generate a new one. The example is only with 3 columns to make it easy to understand.

First, we create a table of Example

create table Ejemplo (
  ID    INT,
  TOTAL_M_01  INT,
  TOTAL_M_02  INT,
  TOTAL_M_03  INT,
  O_01 INT,
  O_02 INT,
  O_03 INT
);

INSERT INTO Ejemplo (ID, TOTAL_M_01, TOTAL_M_02, TOTAL_M_03) values (1,3,5,1);
INSERT INTO Ejemplo (ID, TOTAL_M_01, TOTAL_M_02, TOTAL_M_03) values (2,2,6,7);
INSERT INTO Ejemplo (ID, TOTAL_M_01, TOTAL_M_02, TOTAL_M_03) values (3,6,1,3);

+---+----+------------+------------+------------+------+------+------+
| # | ID | TOTAL_M_01 | TOTAL_M_02 | TOTAL_M_03 | O_01 | O_02 | O_03 |
+---+----+------------+------------+------------+------+------+------+
| 1 | 1  | 3          | 5          | 1          | NULL | NULL | NULL |
+---+----+------------+------------+------------+------+------+------+
| 2 | 2  | 2          | 6          | 7          | NULL | NULL | NULL |
+---+----+------------+------------+------------+------+------+------+
| 3 | 3  | 6          | 1          | 3          | NULL | NULL | NULL |
+---+----+------------+------------+------------+------+------+------+

The idea is to update the columns O_01 to O_03 with the ordered values of the columns TOTAL_M_* .

Create temporary with the values ordered, concatenated and separated by ,

CREATE TEMPORARY TABLE IF NOT EXISTS Temporal AS (
SELECT ID, 
       GROUP_CONCAT(Columnas order by Columnas DESC) ColumnasOrdenadas
       FROM ( SELECT  ID,
                   (case when n = 1 then TOTAL_M_01
                         when n = 2 then TOTAL_M_02
                         when n = 3 then TOTAL_M_03
                    end
                   ) as Columnas
        from Ejemplo a 
        cross join (select 1 as n union all select 2 union all select 3) n
    ) T
    GROUP BY ID
);

+---+----+-------------------+
| # | ID | ColumnasOrdenadas |
+---+----+-------------------+
| 1 | 1  | 5,3,1             |
+---+----+-------------------+
| 2 | 2  | 7,6,2             |
+---+----+-------------------+
| 3 | 3  | 6,3,1             |
+---+----+-------------------+

We already have for each original row, the values of the original columns ordered, now we only have to update the original table

Update the new columns

UPDATE Ejemplo E
       INNER JOIN Temporal T
           ON E.ID = T.ID
       SET O_01 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 1), ',', -1),UNSIGNED INTEGER),
           O_02 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 2), ',', -1),UNSIGNED INTEGER),
           O_03 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 3), ',', -1),UNSIGNED INTEGER);

And now we can see the final result:

+---+----+------------+------------+------------+------+------+------+
| # | ID | TOTAL_M_01 | TOTAL_M_02 | TOTAL_M_03 | O_01 | O_02 | O_03 |
+---+----+------------+------------+------------+------+------+------+
| 1 | 1  | 3          | 5          | 1          | 5    | 3    | 1    |
+---+----+------------+------------+------------+------+------+------+
| 2 | 2  | 2          | 6          | 7          | 7    | 6    | 2    |
+---+----+------------+------------+------------+------+------+------+
| 3 | 3  | 6          | 1          | 3          | 6    | 3    | 1    |
+---+----+------------+------------+------------+------+------+------+

to try, you have this Fiddle

One more help

I will not go into how a stored procedure is defined and if you are doing it right or not, because it is not part of the question and I am not clear about it, what I can tell you is that this solution does NOT You need the cursor for nothing, delete all that part. The only code you would need is the one that you have already adapted from my answer.

-- Creamos y completamos la tabla temporal
CREATE TEMPORARY TABLE IF NOT EXISTS Temporal AS (
       SELECT CODIGO, 
       GROUP_CONCAT(TOT_M_01,
                    TOT_M_02,
                    TOT_M_03,
                    TOT_M_04,
                    TOT_M_05,
                    TOT_M_06,
                    TOT_M_07,
                    TOT_M_08,
                    TOT_M_09,
                    TOT_M_10,
                    TOT_M_11,
                    TOT_M_12
       order by Columnas DESC) ColumnasOrdenadas
       FROM ( SELECT  CODIGO,
                   (case when n = 1 then TOTAL_M_01
                         when n = 2 then TOTAL_M_02
                         when n = 3 then TOTAL_M_03
                         when n = 4 then TOTAL_M_04
                         when n = 5 then TOTAL_M_05
                         when n = 6 then TOTAL_M_06
                         when n = 7 then TOTAL_M_07
                         when n = 8 then TOTAL_M_08
                         when n = 9 then TOTAL_M_09
                         when n = 10 then TOTAL_M_10
                         when n = 11 then TOTAL_M_11
                         when n = 12 then TOTAL_M_12
                    end
                   ) as Columnas
        from PLANILLA_ROTACIONES a 
        cross join (select 1 as n union all select 2 
                                  union all select 3 
                                  union all select 3 
                                  union all select 4
                                  union all select 5 
                                  union all select 6 
                                  union all select 7 
                                  union all select 8
                                  union all select 9 
                                  union all select 10 
                                  union all select 11 
                                  union all select 12) n
    ) T
    GROUP BY CODIGO
);


-- Para verificar antes de actualizar 
-- correr solo hasta este select
SELECT CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 1), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 2), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 3), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 4), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 5), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 6), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 7), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 8), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 9), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 10), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 11), ',', -1),UNSIGNED INTEGER),
       CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 12), ',', -1),UNSIGNED INTEGER)
       FROM PLANILLA_ROTACIONES  E
       INNER JOIN Temporal T ON E.CODIGO = T.CODIGO


-- Si los resultados son los eperados podremos actualizar las tablas definitivas
UPDATE PLANILLA_ROTACIONES  E
       INNER JOIN Temporal T ON E.CODIGO = T.CODIGO
       SET o_01 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 1), ',', -1),UNSIGNED INTEGER),
           o_02 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 2), ',', -1),UNSIGNED INTEGER),
           o_03 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 3), ',', -1),UNSIGNED INTEGER),
           o_04 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 4), ',', -1),UNSIGNED INTEGER),
           o_05 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 5), ',', -1),UNSIGNED INTEGER),
           o_06 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 6), ',', -1),UNSIGNED INTEGER),
           o_07 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 7), ',', -1),UNSIGNED INTEGER),
           o_08 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 8), ',', -1),UNSIGNED INTEGER),
           o_09 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 9), ',', -1),UNSIGNED INTEGER),
           o_10 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 10), ',', -1),UNSIGNED INTEGER),
           o_11 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 11), ',', -1),UNSIGNED INTEGER),
           o_12 = CONVERT(SUBSTRING_INDEX(SUBSTRING_INDEX(T.ColumnasOrdenadas, ',', 12), ',', -1),UNSIGNED INTEGER);