And now it is actually working as you rewritten it, see: https://i.imgur.com/MslJ9s2.png
But since the english version is in the database, that one works for searching only – the turkish version is only a string translation, that is not accessible to search unfortunately.
Well, for the member types maybe using a user meta field to add the turkish text? That way the search could access them – and may even resolve the issue with searching the turkish names, since you could enter those there as well. User meta fields are great for search and can be easily accessed.