How to convert and add mysql date format?

To store into a DATETIME, use STR_TO_DATE() where you describe the format of the string:

 SELECT STR_TO_DATE('Sun Jun 20 00:40:27 IST 2021', "%a %b %d %H:%i:%s IST %Y");
--> 2021-06-20 00:40:27
As a separate step, you can SELECT the Datetime in a different mysql date format using DATE_FORMAT() with a different formatting string.
SELECT DATE_FORMAT('2021-06-20 00:40:27', '%d/%m/%Y');
--> 20/06/2021 00:40:27
You cannot do both conversions in a single function call.
Storing into DATETIME(6) will store 2021-06-20 00:40:27.000000. (In your example, the (6) is wasted.
If you are using LOAD DATA, there is a way to do the STR_TO_DATE as you do the insert.

I don't know how to generalise "IST"; notice that I essentially stepped over it in my sample code.