Saudi-Turkish relations were actually quite bad. The summarize, Turkey of the early 2010s tried to build its own sphere of influence in the middle east by supporting various groups and intervening in civil wars caused by the Arab Spring. There were some short lived successes too. One of the groups Turkey supported was Muslim Brotherhood which was a terrorist organization according to Saudi Arabia. Saudi-Turkish relations were so bad at one point that Saudis were blocking imports from Turkey and not giving visas to Turkish citizens. Saudi Arabia also supported the Greek coalition during tensions related to Eastern Mediterranean.
This all changed after the US started to pull out from the Middle East. Also during these times Covid happened, the Turkish economy went bad and Turkey started to feel really lonely. Saudis were also uncertain about the future at this point. This is when both sides decided to normalize relations. Things look calm now but make no mistake, both sides don't trust each other.
Both Turkey and Saudi Arabia supported Jihadist groups in other Arab countries but not their own. I don't see how this is a difference in position. It's no different to Israel supporting liberal globalist values in America and Europe while they're an ethnostate.
I don't know when you mean when you say America pulled out of the Middle East, they are still there. Turkey stopped the "Assad must go" long before before the GCC countries did once they realised that Americans were arming Kurds who were channelling back into Turkey. The Saudis stuck with it for much longer, but when it became clear Assad was staying they stopped too.
As I said, you gotta be careful if you want to have relations with Gulf states. They are quick to normalize but also they can infamously sell you out. The Saudi-Iran agreement has built up hope for China but dozens of such events happened in the past for no avail. This time the purpose of it seems to be for buying some more time for both sides.
Saudi Arabia have been very stable in terms of foreign relations. They held onto the American pigtails (ahem, cowtails) for as long as America was the number one power. Their rulers have realised America's time is up and are now casting their lot with China.
Unlike that of Turkey under Erdogan, who will backstab anyone and everyone for no reason. Turkey by far is less trustworthy than any Arab country. Is there a major country/bloc in the world that Turkey hasn't had a diplomatic fallout with in the last few years?
One minute Turkey is a close ally of Israel, the next they are threatening them. The same with their relations with EU/NATO and their threats again Greece. Not to mention how things have been playing out with Russia. I can't think of any country as untrustworthy as Turkey, let alone an Arab one.
I think limited cooperation with Turkey is a good idea but they can never be relied upon as an ally by anyone.
