Rifle bedding ideas were different in the blackpowder days. You look at actions and stocks, they full length bedded barrels. This trend continued in centerfire rifles all the way up to the 60's. You can look at pre 64's, M52's (target 22LR's) and you see barrel bands, tight wood to metal fit around the action and barrel.
Modern practice is to let the barrel free float. I have found, and so have many others, that anything touching the barrel, but it bands or stock, will cause irregular vibrations. Sometimes adding a pressure point will "do something" good, but it is rare and is probably specific to a load.
The M1903, along with many service rifles, the fore end tip had five pounds of pressure on the barrel. But, I got to examine some very rare, all original, military team NM 1903's. On a couple they had removed wood from the fore end tip, knocked the upper band screw down, so their barrel was free floated.
I have routed out bedding compound from two hunting older rifles that a previous owner had fully bedded the barrel. Accuracy improved with both rifles.
I believe Mannlicher stocks are pre WW2 things, back then they would have had close inletting and the barrel touching the stock. That is not best practice, but then, you are buying it for the style, right?