On most strategic issues, Turkey and China stand on entirely opposite camps. We may even argue that China, by siding with Russia and vetoing anti-Syrian resolutions at the UNSC, has harmed Turkish government's interests the most.
The US had outsourced Syria to Turkey and Turkey's president had even dreamed of performing Friday prayer in Damascus while then Turkey PM gave President Assad some 3 weeks before he went down.
To this end, Turkey provided every sort of assistance to terrorists from all over the world, couple of thousands being Uighur terrorists -- those resided in China as well as in Turkey. Turkey's government acted practically as a state sponsor of terrorism (as it continues till today). To this end, Turkey government officials provided fake Turkish passports to some Uighur radicals, facilitated their transfer to Turkey via Malaysia, Indonesia and Thailand.
Turkey's state and non-state harboring of small Uighur separatist terror groups continues. Turkey also provides assistance to Uighur majority terrorist groups fighting in Syria under various names in its effort to bring down President Assad.
Now Turkey has been effectively sidelined. Turkey's being kept out of Syrian affairs is a welcome news.
Although China supports (as a historical principle of foreign diplomacy) Turkey's sovereign unity and is opposed to separatism inside Turkey by any groups, Beijing also understands that Turkey, especially under current nationalist-Islamist government, has been harboring separatism (to its own capability, of course, which is not so big) in other
countries, from Syria and Iraq to Libya and Somalia.
Hence, it is practically impossible for China to treat Turkey more than a distant trade partner.
There is very little we really share on the strategic realm with (especially present) Islamist-sectarian and interventionist Turkey government.
Thus, it is not so easy to pivot. It takes two to pivot. China does practically not see with Turkey eye to eye on any important global matters.
On the more social level, China's leadership is entirely different from
Turkey's present bombastic, empire-yearning, sectarian, terrorism enabling and interventionist government. Only if Turkey has secular, peace-oriented, respectful for sovereignty government, then Turkey's pivot (if any) can really mean something to China.
Currently, China sees a better government and more likely partners in Syria and Iran than in Turkey.
If there is going to be a working pivot toward China, that would be Iran pivot. Of course, Iran is a civilization nation, so, they will not even name their policy in such unrealistic way as pivot.
@Serpentine