Not anymore really, at least according to their preference. At a minimum, a capital T will prevent comedic errors like a head full of feathers.

https://www.npr.org/2023/01/08/1147704945/the-state-departme...

Sure, but "turkey" is a bird, not a country. You at least have to write "Turkey" to be clear to English speakers. If you like, save Türkiye for your visits to the UN.