I would say heavily buffed/refinished myself. Who knows?...it could've been refinished more than once?....maybe had been nickeled and then stripped and blued?....may have been heavily pitted at some point and buffed back smooth?....or any combination of the above. I've seen pics of other P08 pistols that were about devoid of the usual markings from a heavy duty refinish. Unfortunate but fairly common on handguns that get rusty and used then made pretty again.

I own an crusty old Weimer era Luger that if you buffed the rust pits off would not be much left of the original markings

The serial number thing I suppose could be an issue...Did you buy the gun from a dealer?...If so he likely just put NSN for the serial #....If it was a private sale deal I would simply keep record of where I got it and not worry about it too much.