Nearly all the short Mauser K actions are radiused behind the recoil lug, some have the small flat too. But, nearly all are small ring actions. The only other known large ring K action, serial Nr. 5340, has the flat behind the recoil lug common with the larger actions. That action is dated 1902, while this one is 1901.
As you wrote, it is marked "V1". This may be a Mauser factory toolroom number. Several other one of a kind Mauser actions are known with such low, V-prefix serial numbers. "V" most likely stands for "Versuch" = test or experiment. So it may well be a toolroom prototype action.
Richard Mahrholdt then was a very influential gun authority besides being a "name" gunmaker and -retailer. He was the original author of the "Waffenlexikon" = gun encyclopedia, a book that was for decades and at least 7 editions "the bible" for German speaking sporting gun enthusiasts. So a Mauser toolroom prototype may well have ended up in his Mahrholdt - Peterlongo shop.
It would be interesting to know about any marks, numbers or letters, under the barrel. Such marks may show if the half - octagonal, ribbed barrel is a Mauser original in 6.5x54, only rechambered to 6.5x57, or if it was added later.
It's a pity that the action was so much reworked, receiver bridge reshaped, tapped and drilled, bolt sleeve and safety altered.
The colour case hardening is certainly not original. It looks a lot like "Turnbull" to me.