It dont matter, 30-06 and 7.62X54R hve the same effect on Bears.
I have caught Dozens of Black, and Brown Bears with both. I currently us a Moain nagant in the Finnish M-39 version and all before it die.
Brown Bear or Barnul Brands of ammo, as well as Winchester load for the 7.62X54R, and EVERYONE loads for 30-06.
Use either with total confidance.
If your using a Mosin Nagant that has a "SA" in a round cornerd square, its a Finish Army property stamp, on the side where the barrel meets the reciver, also, look for a capital "D" stamp as well. The Finns rebuilt Mosins , some with original .310 caliber barrels as teh M-24, later into the M-27 and the M-28 version with a .308 mesurement, but the "D" stamp indicates that the rifle was brought up to spec by armoers, to shoot russian.310-.311, so the Finns could issue captured russian ammo. The final Finn Mosin rebuilds were the M-39 series, and they have .310 barrels.
Theres no danger, but if theres no "SA" in a round cornerd box, then it was never Finish issue or a .308, and its not a big deal anyway.This is sometimes confusing, but when shooting, it dosent matter.
Good luck.