Lets wait and see. China is playing the long term game. The middle-east is too important for China to be left alone. If there is one thing China/East-Asian countries cant stand, it is chaos. Middle-East is notorius for chaos. No peace stays forever there. Time to make order so the energy supply and OBOR project wont be disrupted. USA, UK, Russia and EU had their chance, time to pass the baton to China. Lets see what the future will hold.
The chain reaction caused by separatist as you mentioned would not make a dent in China's ambition as long it suits China's agenda. After the fall of the Sovjet Union, Russia was confident and content to have the possibility to control all the central asians countries. Nowaday it is China who is controling the central asian countries via OBOR AIIB and SCO. Same situation with South East-Asian region. What make you think the middle-east region would be so different to handle once China sets its eyes on the region? Your mistake is to think Turkiye is in the same league as China.
https://www.ft.com/content/4a9b008a-c2be-11e9-a8e9-296ca66511c9