No. That's what I meant when I wrote your barrel profile being different from any original Mauser, Oberndorf, commercial barrels. All the originals were "stepped". Most early ones are like the one shown above by Xausa, others like my 1933 vintage B in 7x57 on an intermediate action. No Mauser round barrel had a straight taper like your's. I guess, your stock contained a half-octagonal, ribbed barrel originally.

BTW, you seem to confuse "intermediate" and "transitional" Mauser actions. Those early small ring test actions like your's, still without the bolt sleeve lock and the safety firing pin, are called "transitional actions". "Intermediate actions" have a bolt about 5 mm shorter and a receiver ring correspondingly longer than the standard length M98 actions of the German military rifles and copies. Though some transitional actions are of intermediate length too, intermediate actions were used by Mauser on 7x57 and .275 rifles as made for Rigby, as well as Turkish M1903 and Peruvian M1909 military rifles in 7.65x53.
Mauser rear sight bases were not soldered on "saddles" like your's, but part of a sleeve/ring soldered over the barrel and closely fitted against a step. You can barely make out the seam just behind the rear sight base on my rifle, but not visible in a photo.