No, it was not done with a gentle nudge. It was done by Massacre and Genocide, before the word Genocide existed.
So, yes all those genetic elements exist in Turkey, but not in all groups. Some of these were know from the beginning of Turkey in 1915, but now talked about because of Islamification. But is was always present if you presented a problem for the state, they would threaten or use the records to ruin your life.
Prior to 1915 the Ottoman rulers did the same thing on a whim. But from the beginning neither the Ottoman rulers or the Turks ever admitted a single Massacre.
So, here we are again. Certainly it is in Efrin (Afrin) Syria.
I think the genetics might’ve changed a great deal after the Turkish conquest in the Middle Ages, because before that, under the Byzantines, central Anatolia was more urban and settled, but after the Turks, it went to pasture and wilderness, and the urban and farming population moved toward the coasts.
At least that what I gathered from history. It’d be interesting to see if there’s a genetic footprint there.
Also, under the Byzantines, there was a lot of resettling captured people, as well as people from places conquered by the Muslims. But whether there was enough of that to change the genetics, I don’t know.