The damage the Mongols did to Asia was, on the whole, superficial. The number of Mongols was very small relative to the populations they conquered, and they were content to skim wealth off the top in most cases. Certainly some local areas were “made an example of,” and in those particular places it might have taken generations to come back.
In most cases the devastated civilization winds up getting replaced by something else, and the survivors assimilate themselves into the new order. Many observers see this on the horizon in Europe today as more immigrants and their descendants change the culture and system. I don’t think we can chalk all of that up to the world wars, but certainly they contributed to the process in the longer term.
Off the top of my head, I can’t think of a civilization that bounced back in essentially the same form after a really severe trauma like that. What comes next is always substantially different. There are degrees of continuity depending how much the trauma is internal and how much is external, though.
I hope this helps.