Ottoman empire was a bit of a weird phenomenon in history. In many ways because they were originally a nomad empire and the core Turkish population was not that big. While the empire was huge and it had a large population it wasn't really that big after all. Large part of the area of the empire was basically desert. At its height the whole population was a bit larger than population of France and a bit smaller than that of the holy roman empire. And most of the population was not Turkish, which is why it was probably a good move to strongly include the other ethnicities in the government and adopt their ways rather than trying to impose their own. At least in the beginning.

The Turkish nobility wasn't very loyal to the sultan and the sultans themselves were often quite weak. The sultans secured their positions by recruiting "Devshirme", who were mainly boys from Balkan Christian cultures recruited to the army or government offices as a child. These "foreigners" basically ran the empire from military generals to bureaucrats. They were mostly loyal to the sultan but also pushed the Turkish nobility out of power weakening the influence of the Turkish culture and creating a degree of resentment among the Turkish nobles. The Devshirme also grew to be very powerful in the weakness of the sultans and they created their own political factions which started to control the political appointments to further their own ends rather than those of the empire. For times the Sultans were basically powerless when this political machine (again comprised entirely of people who were neither Turkish nor Arab) did all the decisions.

What made the empire so strong around the times of Suleyman the magnificent and some time after was that hey were fabulously rich and could therefore more easily afford to raise massive military forces without going bankrupt like most European powers did many times. This was because of their control of all trade to east. All the gold and silver in Europe flowed to ottoman empire to buy luxury goods like silk and spices (like almost literally all, much faster than more could be mined, which caused a major economic crisis). And this was also the key to their downfall. The Portuguese found a route around Africa and built trade depots along the way. The Spanish on the other hand came to a new continent with all its riches in their effort to find a way around the ottomans. Italians built domestic production of things like silk. The old monopoly position was broken more and more as sea routes developed and they were left with an empire that was used to being fabulously rich but was no longer actually quite that rich. An empire with a political structure built to secure the Sultan but which left him almost powerless while concentrating in infighting and political squabbles rather than efficient ruling.

All in all the empire, after its rise to power, was never really Turkish. They never drove a clear distinct culture because the government simply didn't have one. The government was largely a hodgepodge of people from the Balkans who were taken as a child and raised in the Sultan's court and had their own weird culture disconnected from the reality of any of the peoples of the empire.