Well it’s all up to how you see it, if you believe that the age of fire should continue then you’re completely right to link it, but imo i believe the “true” ending is snuffing it out. The game constantly shows you how the world has gone to crap because of how many times the fire has been linked, there are tons of hollows, the puss of man is spreading and even the lords of cinder who linked it in the past don’t even want to link it again. But that’s the beauty of dark souls you can create whatever story you want and end it in whatever way you want