Should I include setState in useCallback's array of dependencies?

The recommendation for that is also on React Docs - Hooks API Reference.

The setState function is used to update the state. It accepts a new state value and enqueues a re-render of the component.

setState(newState);

During subsequent re-renders, the first value returned by useState will always be the most recent state after applying updates.

Note

React guarantees that setState function identity is stable and won’t change on re-renders. This is why it’s safe to omit from the useEffect or useCallback dependency list.