Hi Andrey,
Yes it is correct that it is required to use cookieDomain for multi-part, top-level domains where either of last 2 parts of the URL are > two characters. The "www" prefix is not required when instantiating this variable.
if you do not put cookieDomain = domain.com.tr then the cookie will be set on com.tr
You DTM configuration seems to be correct.
For the data element I will suggest you to specific custom value if domain like domain.com.tr else return default base domain. you can also return "", it will put the cookie to the default base domain, I tested and it works.
Best regards.
Alexis Cazes
Lead Technical Support Engineer