getDerivedStateFromProps does not look like the right tool for what you are trying to do. Instead use componentDidUpdate:

componentDidUpdate(prevProps) {
  const { date } = this.props;
  if (prevProps.date !== date) {
    this.getList(date);
  }
}

It's pretty rare to use getDerivedStateFromProps. For more information on when to use getDerivedStateFromProps I recommend this article

About the removal of componentWillReceiveProps: you should be able to handle its uses with a combination of getDerivedStateFromProps and componentDidUpdate, see the React blog post for example migrations. And yes, the object returned by getDerivedStateFromProps updates the state similarly to an object passed to setState.

In case you really need the old value of a prop, you can always cache it in your state with something like this:

state = {
  cachedSomeProp: null
  // ... rest of initial state
};

static getDerivedStateFromProps(nextProps, prevState) {
  // do things with nextProps.someProp and prevState.cachedSomeProp
  return {
    cachedSomeProp: nextProps.someProp,
    // ... other derived state properties
  };
}

Anything that doesn't affect the state can be put in componentDidUpdate, and there's even a getSnapshotBeforeUpdate for very low-level stuff.

UPDATE: To get a feel for the new (and old) lifecycle methods, the react-lifecycle-visualizer package may be helpful.

Why don't you use componentDidUpdate for this? It seems to me you can achieve the result by:

/**
 * @param {Props} prevProps props of the component
 **/
componentDidUpdate(prevProps) {
  if (prevProps.myStateVar !== this.props.myStateVar) {
    this.setState({ myStateVar: this.props.myStateVar });
    toggle();
  }
}

First, in your componentWillReceiveProps example, you shouldn't be setting state directly. Instead, you should be calling this.setState.

However, to answer your question... are there reasons you wouldn't choose to do this in componentDidUpdate? That might be better than using getDerivedStateFromProps.