How is Germany divided?

Did you see the areas that voted far right? Lots of overlap with firmer East Germany

That would not be a split in halves, by any means, though. East Germany accounts for about 15% of the population, last I looked. Also, the far-right AfD got about 20% of the votes in the recent election. That is also not a split in halves.

Why squabble at semantics here fixating on exactly half? 1/5th of modern Germany voting for the modern incarnation of the nazi party is a disgrace and speaks to the propaganda situation their population faces.

Simply because the statement was "half of the population benefits [..]". That is wrong. Feel free to skip corrections that annoy you.

East and West. The differences in economic output and political leanings are stark.

You can see for yourself: https://bundeswahlleiterin.de/bundestagswahlen/2025/ergebnis... This shows the winners of the "second vote." Dark blue = CSU (conservative party), its outlines are identical to Bavaria because this party only runs there and, this time around, won 100% of the second votes. Cyan = AfD, far right-wing party. Its outlines are nearly identical to the borders of the former GDR. Gray = CDU, CSU's sister party, making up for most of the remainder.

You effectivly can just ignore the differentiation between the CSU and the CDU, they are mostly just referred to as "Die Union" (the union).