When I bought a M1941 Carcano rifle at the Appalachian Trade Fair (back in the time When Dinosaurs Ruled the Earth, 1970), the only readily available ammo in 6.5 Carcano was Norma of Sweden 160gr softnose with .264" bullets same as their 6.5 Mannlicher Schonauer. One box of twenty Norma 6.5 Carcano ammo cost more than what I paid for the rifle. I quickly acquired a classic Lee Loader kit for it. Rechambering Carcanos for the more readily available 6.5 M-S was actually a thing back then but I did not see the point of rechambering the barrel when I can reload cartrdges (my Hornady manual showed the 6.5 Carcano (21" bbl) & 6.5 M-S (18" bbl) with 30 gr IMR 3031, .264" 160gr as giving 2100fps & 2000fps).
Also back in them thar days it was 6.5 Italian or 6.5 Carcano not 6.5x52mm and 6.5 M-s not 6.5x54mm and .30 Carbine not 7.62x33mm. This younger x generation and their NATOizing traditional cartridge names with xmms, bah, humbug.
Whether .268 bullets work better than .264 bullets in a Carcano rifle depends a lot the condition of the bore of the individual Carcano rifle. I don't see any difference in group size between reloads with .264" vs .268" bullets in my M1938 short rifle. I have learned to match 6.5 Carcano cases by neck thickness to bullet diameter, using Norma casings with .264" bullets, Graf casings with .268" bullets and not mixing them.