The citizens of Turkey are 90% Byzantine converts to Islam. Barely any Central Asian Turks, much like Azerbaijan. They speak Turkic, that is about it.
The Ottomans would care about what is happening in China because they are part of the 10% non-Byzantine converts to Islam.
Turkish citizens caring about and crying over what China is doing to a Chinese minority - Uighur Turks is like Native Americans in Canada crying over the Irish treating the British badly in Northern Ireland. And then asked why, the Native Americans say they Native Americans speak the English language and those that speak English must stick together.
The Byzantines graciously and rightly accepted the Muslim religion, but to identify as ethnic Turks when 90% of them have maleline ancestors going back to the Roman Empire, needs to be addressed. Erdogan once stated he was of Georgian origin, then had to clarify he was a Turk. Of course he is a Turk, he is living in Turkey and identifies as a citizen of Turkey, not some traitorous minority like many of the Kurds. But Erdogan is no Ottoman or someone from Central Asia. Erdogan's ancestors were part of the Byzantine Empire and before that Roman Empire and before that probably some Greek colonist. This is the history of most in Turkey.
May Erdogan be the new Sultan, the native Sultan of Turkey. He is far better than any of the Kamalists.
