Its actually a reference to the rivers of blood Katana in elden ring.
Weapon of Okina, swordsman from the Land of Reeds.
A cursed weapon that has felled countless men.
When Mohg, the Lord of Blood, first felt Okina's sword, and madness,
upon his flesh, he had a proposal, to offer Okina the life of a demon, whose thirst would never go unsated.
Basically, its stained red and black because thats how many people were killed by it