wanted to verify that during the black death, people not only gained more benefits but now have more stable lives than before it and thus defeating the plague and gaining vast knowledge

I'm curious as to how the game frames any of this, especially how surviving the Black Death lead to the gaining of 'vast knowledge'. The thing is that nobody 'defeated' the Black Death, they simply survived it, and certainly not by 'discovering' the middle class.

There is some historical veracity to the Black Death improving the living conditions of those who were fortunate to survive it. It's hard to overstate the impact of the plague itself: it killed roughly a third of the population of Europe, and in some major cities and ports, it would kill over 40%. What this meant in the aftermath was that there was a severe labour shortage, especially among skilled craftspeople. In turn, with their labour in high demand, workers were far better placed to demand better pay and conditions than they had enjoyed prior to the Black Death. This was a consequence of the Black Death rather than a means of halting it however, and the idea of discovering the Middle Class is somewhat of a fallacy.

We tend to posit a middle class as a modern/early modern phenomenon, but there has always been a middle class of sorts, albeit a much, much smaller one than today. During the Medieval period, this class consists mostly of merchants, traders, scribes, royal officers, and various tradespeople and farmers, of what we could term the higher order of peasantry. In Early Medieval England, for example, Freemen were the wealthiest of the peasant class who owned their land outright and as a result could be quite wealthy. Other middle class individuals were those who could be found in urban environments: craftsmen, jewellers, goldsmiths, administrators, traders and suchlike.