Maybe I can take the weight from my compatriot and tell you this: genetically speaking, Turks are very much European and Middle Eastern, not Central Asian. Anatolia, for almost all of its history, had been a major destination of migration. For the last 200 years alone, we had seen huge waves of migrations from Balkans and Caucasus, and despite these people had a culture very different to ours, Turkish Culture integrated them and so; all of these people are Turks, even though none actually are. In the future, we would see how staying Syrians would experience a similar phenomena; just like how Albanians, Circassians, Laz and Lezgi of the Black Sea, Arabs of Hatay and Adana and heck, most of the Kurdish integrated into the greater national umbrella, that is Turkish identity. Knowingly or unknowingly, most Turkish actually cherish that, as we have a saying in Turkish claiming we are a nation of 72 ethnicities. So no, racially speaking Turks do not resemble our cousins in Central Asia at all.
That being said though, the most uniting factor of Turkish nationality is the language, which is of course, Turkic. In fact, Turkmen and Azeri is 99% intelligible to Turkish speakers and from music to food, we have much in common. Starting from the Tiele and Dingling of Siberia, we shared the same history. In fact, the cultural exchange between Anatolia and Central Asia was intact until the Russians settled to region properly, so even though we might be distant (or not as close as we used to be) now, this is a recent development. We should open the communications that were happening in the past, and encourage cultural exchange with these people. We are a vibrant, culture-producing, science-producing nation. We should capitalize on that and show our cousins that they don't have to depend on the bear, as the wolf too can be great on its own.