How do I return identical values between two string aggregated columns in SQL?

I have 2 columns A & B in a SQL Server table that contain a string aggregated list of codes.

The codes in the lists are separated by a semicolon.

The string aggregated lists can take any length and the codes can be in any order.

What I would like to do is to create a new column C which contains the codes that appear somewhere in the same row of the lists of Column A and Column B.

Example:

The example above returns "c", "a" and "e" for the first row of column C, because these codes are present in the same row of both Column A and Column B.

The same for the second row, here "e" and "d" are overlapping in Column A and B and thus returned in Column C.

I have tried something that works, but it does not seem like the best solution in terms of efficiency and performance. Especially because I have many (1m+) rows to check this for and the length of code lists to compare can be very long.

SELECT 
    STRING_AGG(CAST([value] AS NVARCHAR(MAX)),'; ') AS Overlapping_Code 
FROM
    (SELECT a.value 
     FROM MyTable t 
     CROSS APPLY STRING_SPLIT(t.Column_A, ';') a

     INTERSECT

     SELECT b.value 
     FROM MyTable t 
     CROSS APPLY STRING_SPLIT(t.Column_B, ';') b 
) ab

I am looking for a better solution in terms of performance and elegance to compare the string aggregated lists for two columns across (many) rows.

Here is another possible solution:

CREATE TABLE MyTable (a VARCHAR(100) NOT NULL, b VARCHAR(100) NOT NULL /* PRIMARY KEY ?? */);

INSERT INTO MyTable VALUES ('a;b;c;d;e','c;a;e;i;k'),('d;e;f;g','e;h;i;j;d');

SELECT *,
    (SELECT STRING_AGG(x.value,';')
    FROM STRING_SPLIT(a,';') AS x
    , STRING_SPLIT(b,';') AS z
    WHERE x.value=z.value)
FROM mytable AS t;



a          b          c          
---------- ---------- -------
a;b;c;d;e  c;a;e;i;k  c;a;e
d;e;f;g    e;h;i;j;d  e;d