From the looks of the pictures, it does look like the rifling has been worn away at the muzzle, and the rifling looks like rounded off. That said, it also looks like there is still good rifling in the bore.
I would have a Gunsmith recrown the barrel. If it is really worn back inside the muzzle area a bit, it would be possible to counterbore the muzzle back about 3/4 to one inch, and get sharper rifling. The practice of counterboring a muzzle to get accuracy was well practiced in Finland and Russia, and you can find many Mosin Nagant rifles that have a bit of a bulge in the muzzle area of the barrel where an obstruction (Snow) was when the rifle was fired. Finnish Armourers had a kit for counterboring a rifle muzzle so that a rifle was returned to service in a minimum of time.
Mauser rifles generally have some deep rifling, and even a bore that looks crappy can shoot with acceptable accuracy. Buy a can of foaming bore cleaner, such as "WipeOut," and follow the directions on the can for best results. It is amazing what that stuff will do to clean a bore, and you might be pleasantly surprised.
As far as the thinking of altering the rifle to a sporting configuration by installing a new barrel, that is false economy. Not only do you have to figure in the cost of the barrel and it's installation, but also drilling and tapping for scope mounts, bending the bolt, an other alterations. You would be lucky to get away with $500 and then still have it in the Military stock. It is possible to buy a more suitable sporting rifle today, new, for $300 for a Savage Axis, $400 for a Ruger American or the new Remington model designed to compete with the more moderately priced market, or a good used hunting rifle on the EE.
The rifling on your rifle looks damaged a bit deep in the muzzle for the average "touch up" crowning with a round ball abrasive at home, especially if someone is a bit new at repairs and alterations, but a good Gunsmith with a metal lathe could easily counterbore and/or recrown the barrel.
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