I think the most important thing is to be consistent, instead of having a mix of API logic that originates from components and from the store. And since there are certain types of higher-level logic that are very difficult to house inside components, I have found that having your store be the origin for _all_ API-related logic is the best way to go, even if it seems overkill for simple things. It's better to be globally consistent than to try to have the simplest solution for every individual case.

(Disclaimer: I use React/Redux and not Vue/Vuex, but I think the above applies equally to both.)