When a component re-renders due to a state update or props change, React will re-evaluate the component function and render the component's output again. This includes any child components that the parent component renders.
In the example you provided, if the parent component uses useState, and a state update occurs, then the parent component will re-evaluate and render its output again. This will also cause any child components that the parent component renders, including the component, to be re-evaluated and re-rendered as well.
However, it's important to note that even if a component re-renders, React will try to optimize the rendering process by minimizing the number of DOM updates that need to occur. React uses a technique called "reconciliation" to compare the previous and current output of a component and determine which parts of the DOM need to be updated. This means that even if a component and its children re-render, not all of their output may actually result in DOM updates.
In general, using useState in a parent component should not cause significant performance issues unless the component hierarchy is very deep or the child components themselves are very computationally expensive to render.