Turkiye doesn't care about a second cold war. Erdogan is using this as leverage to try and force Sweden to get tougher on Kurdish militants. In other words Turkiye cares about Turkiye and nothing more (which is fine .. most countries do that).
Yeah, Erdogan is just milking this scenario as much as he can. Perhaps he's finally getting his F-16s and moves on to the next big thing that keeps focus of the cluster fuck of an economy he's got going on.