Europe is the most affected as 60 years after the end of the Second Global War, it's still a poverty stricken area. It has not fully recovered. Europe would be comparable to OTL Somalia or OTL Syria.
True that Europe is not fully recovered from 20 years lasted WW2 but it would be insulting to say that they are not better than Somalia or Syria. Many European countries would have living standards of Latin America. And few would have even comparable to OTL Eastern/Mediterranean Europe. But still ot of better than Somalia. Such comparison might had been true in 1960's but it would be better in 2023.
How about Europe as of 2100 AD?
Hard to say. My prediction until 2100 about Europe: China launch its bioattack sometimes in 2020's or in 2030 at latest. It devastates lot but not much worsely than Spanis Flu. Europe would still climb towards. After German statelets have paid all of their reparations by 2060 them have allowed bit bigger independence but unification is still stricktly barred altough there might be some pro-unification movememtens but they are pretty much pacifist movements.
Russia might has annexed Soviet Union after it has became basically dead nation.
What country could be a dominant power in the European continent as of 2100?
Probably there is just bunch of local powers instead one or two one. Of course Britain would be still strongest European country but local powers probably would are Spain, Italy and perhaps Poland. Finland could be too such since it has lot of resources and better economy even in 2023 than mediocre European country. France could be possible too but it should collect its shit.
Is it likely that dialects of Rhenish, Low German, and Bavarian would become standard languages, thus leaving German as an extinct language?
I only assume that German language would be dead, only for successor such as Austro-Bavarian, Rhenish, Low German or Saxon, and Swiss to be diverged.
I bit doubt that German would happen such thing what for Latin did. The language would be still used on inter-statlet trade and diblomacy. And people probably would still move between statelets. So there hardly is much divergment at least by 2100. It would be too short time.
Italy, Spain, Portugal, Greece, and Poland. Poland is already on its way to a regional power. It bounced back after taking vengeance on the Reich.
I am not so sure about Greece. Even in OTL it is still pretty weak and economically not really strong. But these other nation perhaps could are pretty succesful. And Bulgaria could be too pretty succesful local power. Perhaps Croatia too.
Well, stricktly spoken Turkey is not European country. But definitely Mediterranean one yes. It has some chances to become such powerhouse than in OTL.
Just wondering how Turkey is treatening its Kurdish population. Definitely it has take softer stance since A4 would go easily pretty mad. And how Turkey is dealing with Armenian Genocide? I would suppose that Turkey is not that denial about that but not sure would it still admit such thing.