I'm 100% not used to Türkiye spelling, but find it logically useful that it undo confusion between the country and the bird. The birds as well as some verbs tend to sneak into dropdowns when devs cheap out and paste language resource files to Google Translate or ChatGPT.
That only applies to english though. In dutch the country is called Turkije and the bird is called a kalkoen. I'm sure in by far most languages there's no confusion between the bird and the country, and yet everyone across the whole world gets told to spell it Türkiye.