"(that the barrel extension was applied after proof) and don’t address the question of “why?”"
Ok, the why on this example is that it was numbered in the military style when re-worked by the police, since it did not have a serial number on the receiver(1920 commercials do not), the 4 digits without suffix were added. This is not "speculation".
This example is not an "abberant" gun, there are many examples of such added numbers; I have several myself and another on the way.
This is all explained in the three volume work by Goertz and Sturgess, with many references to the original German regs and requirements.
Here are pictures of a few police "reworks" I have with the added serial digits to the left of the chamber, and a couple that did not get them added. Remember that most of these reworks were refinished after the work, and all the markings are typically "under" the finish.
Hope this helps.