Learn Hardcore Turkish: Yeni proje için Ali terfi aldı. - Ali got a promotion for the new project.

İçin means “for” and introduces purpose/beneficiary. So yeni proje için = “for the new project” (i.e., with the purpose of staffing or serving that project). It can sometimes be read as a reason, but purpose is the default reading with için.

Why doesn’t Ali have any case ending?

Ali is the subject, which is in the nominative case in Turkish and is left unmarked. Only objects (when definite) and certain complements get case endings.

Why doesn’t terfi have the accusative ending (-i)?

Because it’s an indefinite direct object: terfi aldı = “(he) got a promotion.” If you make it definite, you add accusative: terfiyi aldı = “(he) got the promotion.”

Is terfi almak an idiom? Can I also say terfi etmek?

Yes. Both are common:

terfi almak = “to get a promotion”
terfi etmek = “to be promoted” They’re near-equivalents in everyday use. In formal HR language, you’ll also see causatives/passives like terfi ettirildi (“was promoted [by someone]”).

How do I say “Ali was promoted to manager”?