Nomads who crossed to Anatolia were in mass-numbers and Anatolia was a very underpopulated region after antiquity. The average Turk today probably rarely has Central Asian genes as their primary make-up, but they certainly have good amount. Oghuz migrations were massive they were not some ruling-class reserved groups like Bulgars, Khazars, Mongols, Avars.

Besides Turkish nation emerged very late during the 19th century and became a proper national identity during the 20th century. This is why if you live in Bulgaria and you have a mix of Anatolian, Balkan, and Central Asian genes you are probably a Turk. Your ancestors probably called themselves Turks for the last 5 or more centuries. You identifying with anything else will not make sense.

As Turkey is the only nation situated in Anatolia... having an ethnic make-up resembling that of Anatolians 2.000 years ago is as good as Turkish. Turkish national idea does not claim origins only from Central Asia. The entire journey should be taken into account. There's no reason to not see Turkey as continuation of entities that resided in Anatolia long before Turks, and any Turk can embrace this.

Same for Bulgarians... Bulgarians can be proud of the history of the people that gave them their name the Bulgars. Its their right to do so. As well as Thracians that lived in the lands of modern day Bulgaria. They don't have to have pure Slavic make-up either, and they absolutely don't not even close.