The "fluted" firing pin was introduced, as you mentioned, by Mauser in the 1930s. This relief helped prevent damage to the breech block rear when gasses blew back through the primer if it was punctured.
Matching firing pins of earlier Lugers would not be expected to have this fluting. It is normal, and not an indication of privatization.
It is also a reason for considering getting a fluted firing pin for older Lugers that you intend to shoot.
Marc
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 Igitur si vis pacem, para bellum -
- Therefore if you want peace, prepare for war.
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