Doctrine 2 (used in Symfony v6) : impossible to use "GROUP BY" with "CASE WHEN ..."

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On my website, I build a complex DQL query (more than 200 lines). This DQL query works like a charm.

Now, at the end of the query, I want to GROUP BY some results depending some values of some columns. Here a simplified example :

# the content of a table

+----+------+------+------+------+
| id | col1 | col2 | col3 | col4 |
+----+------+------+------+------+
|  1 | a    | 1    | foo  | NULL |
|  2 | b    | NULL | foo  | fuu  |
|  3 | c    | 2    | NULL | foo  |
|  4 | d    | NULL | foo  | foo  |
|  5 | e    | 1    | foo  | NULL |
|  6 | f    | 4    | NULL | NULL |
|  7 | g    | 3    | faa  | NULL |
|  8 | h    | 2    | NULL | foo  |
|  9 | i    | 2    | NULL | foo  |
| 10 | j    | 3    | faa  | NULL |
| 11 | k    | 2    | NULL | fii  |
| 12 | l    | 4    | NULL | NULL |
| 13 | m    | 1    | foo  | NULL |
+----+------+------+------+------+

# Below, the result expected after query : 
> I group by col2 : 
    - except when col2 contains NULL value 
    - if col2 is not null AND
        - col3 is not null
        - OR 
        - col3 is null AND col4 is not null
    

+----+------+--------+--------+--------+
| id | col1 |  col2  |  col3  |  col4  |
+----+------+--------+--------+--------+
|  1 | a    | 1      | foo    | (null) |
|  2 | b    | (null) | foo    | fuu    |
|  7 | g    | 3      | faa    | (null) |
|  4 | d    | (null) | (null) | foo    |
|  6 | f    | 4      | (null) | (null) |
| 12 | l    | 4      | (null) | (null) |
+----+------+--------+--------+--------+

With SQL I can easily handle that with "GROUP BY" and "CASE WHEN...":

SELECT *
FROM mytable
GROUP BY CASE
    WHEN col2 IS NOT NULL AND ((col3 IS NOT NULL) OR (col3 IS NULL AND col4 IS NOT NULL)) THEN col2
    ELSE id
END

You can try it here if you want

On Symfony (version 6) and Doctrine (version 2.9), I already use "CASE WHEN..." with the doctrine method addSelect(...). (and its work)

But, now, I want use "CASE WHEN..." in the method addGroupBy and its not work ans I don't understand why... (maybe a doctrine limitation ?)

From my repository, in DQL query, if I try to use "CASE WHEN" with a groupBy like this :

$query->addGroupBy('CASE WHEN content.periodicity ...')

I get the error :

[Semantical Error] line 0, col 205 near 'CASE WHEN content.periodicity': Error: Cannot group by undefined identification or result variable.

For debugging, I get the SQL query generated by doctrine from profiler bundle, then I add manually the SQL part GROUP BY CASE WHEN content.periodicity ... and try it from a database software (I use DB Browser). And all work without any error :

For information, the link between 'content' entity and 'periodicity' entity is ManyToOne. I tried to change content.periodicity by content.periodicity_id but I get the same error.

My questions :

1. Is a limitation of Doctrine (v2.9) ? In other words, Doctrine can't use CASE WHEN ... with GroupBy ?

2. If no, what/where is my mystake ?

3. if yes, is it possible to insert native SQL part in a DQL query ? (if yes, I'll can add 'manually' in my code the SQL part GROUP BY CASE WHEN ...)

Thank for any help :)