I agree with this question and answer it. In the case of German and English, since the same alphabet is used, there may be ambiguity when judging the user's intention, but in the case of Korean users, they will not expect a Korean site to come out as a result of the search while searching in English.
Fortunately, if the region is set as "international", it seems to operate similarly to what is desired.
I don't use Roman alphabets such as Japanese, Chinese, and Vietnamese, and I think users from other countries where the language is mainly concentrated in one country will expect a similar experience as me. Although it is controversial depending on the user's country what initial regional setting is good, since Kagi is a membership search engine, wouldn't it be an alternative to explicitly ask about the user's expectations during the sign up process?