The pan is part of the recipe. Pouring the same batter into a much wider tin makes a shallower bake, while a smaller tin can leave the middle underdone after the edges have colored.
Check the dimensions before you start. If substituting, use reliable pan-conversion guidance and expect to adjust monitoring rather than copying the original time blindly. Do not fill a pan beyond a safe level in the hope that the batter will politely stay inside.
Material matters too. Dark metal, light metal, glass, and ceramic transfer heat differently. Follow the recipe and pan manufacturer's recommendations where available.
For your first attempt at a new vegan cake, keep the pan and ingredient types close to the instructions. Once you know the intended texture, it becomes easier to judge whether a later change has helped or simply produced a different bake.