Q. How do I organize sources in a bibliography from different alphabets?

APA

For APA, follow what was outlined for non-Latin scripts on the APA style blog: https://blog.apastyle.org/apastyle/2018/09/how-to-quote-a-foreign-language-source-and-its-translation.html

Chicago

Author(s), year. Title in original language (if possible) [Title translated into English]. Publication name in original language (if possible) [Publication name translated into English]. Volume/issue/page information (according to type of publication). [In ‘language’].

and as an example:

Krenke, A.N. and Khodakov, V.G., 1966. O svyasi povercknostnogo tayaniya lednikov s temperaturoy vozdukha [On the relationship between melt of glaciers and air temperature]. Materialy Glyatsiologicheskikh Issledovaniy [Data of Glaciological Studies], 12. 153–163. [In Russian].

MLA

For MLA, follow what is outlined on their website: https://style.mla.org/nonroman-characters/