As the war drug on, the Germans began using about any decent handguns they could get their hands on. I suspect that the main reason that they used so many .32's is because there were simply a lot of arms factories in countries like Czechoslovakia, Yugoslavia, Poland, and others that they invaded that were already tooled up to make .32 semi-autos.
Not quite. As the war drug on and even early on, they had a tremendous need for handguns. The main reason for 32 being common is because it was standard. Before WWII and even during WWI there were tons of different 32s. The Sauer 38H, PP and PPK, Mauser HSc, Mauser 1934, and many others were all 32 in their base forms. These were all German designs.
The 32 instead of caliber X had nothing to do with the occupying countries. The reverse is actually true. For example, Germany annexed Czechoslovakia in 1938 and invaded Hungary in 1944 (who was an ally and member of the axis powers before that). In both instances, pistol wise, the Germans mass produced 32s in these countries' factories rather than their own 380s which both countries had issued. Ever notice how a CZ 38 is 380 and a CZ 27 is 32, and yet nearly all of the German CZs are 27s? Why would that be? Its because they wanted 32s produced, not 380s. It was not because CZ 27s were the latest and greatest being made for the Czechs. The Czech army was going to adopt the CZ 38 as standard issue. Also, the Femaru pistol in its original Hungarian form was 380, but once again the Germans designated it the P.37 and had it chambered in 32 acp.
Also, FWIW, I know of no Polish 32s issued by the Nazis nor do I know of any Yugoslav 32s thay were issued. Many of the foreign 32s that the Germans had were from Belgium (FN), Italy (Beretta), Hungary (FEG), France (Unique, MAB, SACM) and a few other pistols made in much smaller numbers such as the Spanish Astra 300.
Here are my two FN 1922s, both WaA140 with an original Hungarian 37M in 380. It does not have the German markings.
Right CZ 24, middle 2 are CZ 27, the phosphate one is WaA76 on the right a CZ 38. That CZ 38 has one of the most beautiful blue finishes of all of my guns.