Is it correct to use await setState()?

You can't await this.setState for the reasons already stated. But you can write your own awaitable setState function easily:

promisedSetState = (newState) => new Promise(resolve => this.setState(newState, resolve));

now you can call

await promisedSetState({ someState: true });

No this.setState doesn't return a promise.

So you can't use await in this case. You need to use the callback.