Can I update a React component's props such as a className due to an event like a click? It seems impossible since the component is rendered.
yes, you can.
create a state and keep className:
const [elmClass, setElmClass] = React.useState("first");
use className and update it onClick:
<div className={elmClass} onClick={() => {setElmClass("second")}>
Change my className
</div>
take a look at this example: