getDerivedStateFromProps is not a direct alternative to componentWillReceiveProps, purely because of the fact that its called after every update, whether its the change in state or change in props or re-render of parent.

However whatever is the case, simply returning the state from getDerivedStateFromProps is not the right way, you need to compare the state and props before returning the value. Else with every update the state is getting reset to props and the cycle continues

As per the docs

getDerivedStateFromProps is invoked right before calling the render method, both on the initial mount and on subsequent updates. It should return an object to update the state, or null to update nothing.

This method exists for rare use cases where the state depends on changes in props over time. For example, it might be handy for implementing a <Transition> component that compares its previous and next children to decide which of them to animate in and out.

Deriving state leads to verbose code and makes your components difficult to think about. Make sure you’re familiar with simpler alternatives:

If you need to perform a side effect (for example, data fetching or an animation) in response to a change in props, use componentDidUpdate lifecycle instead.

If you want to re-compute some data only when a prop changes, use a memoization helper instead.

If you want to “reset” some state when a prop changes, consider either making a component fully controlled or fully uncontrolled with a key instead.

P.S. Note that the arguments to getDerivedStateFromProps are props and state and not nextProps and prevProps

To get into more details,

In order to make changes based on props change, we need to store prevPropsState in state, in order to detect changes. A typical implementation would look like

static getDerivedStateFromProps(props, state) {
    // Note we need to store prevPropsState to detect changes.
    if (
      props.myPropsState !== state.prevPropsState
    ) {
      return {
        prevPropsState: state.myState,
        myState: props.myPropsState
      };
    }
    return null;
  }

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

how would I get to know if the props really got changed.

Compare previous prop with new prop.

For simplest use case, just use componentDidUpdate(), with prop comparing:

componentDidUpdate(prevProps) {
  // Typical usage (don't forget to compare props):
  if (this.props.userID !== prevProps.userID) {
    this.fetchData(this.props.userID);
  }
}

According to React Doc, it is OK to perform side effect or setState() inside componentDidUpdate().

And setState() can cause re-rendering, which affects component performance. When performance in this case is actually a thing, read on: https://reactjs.org/blog/2018/06/07/you-probably-dont-need-derived-state.html#when-to-use-derived-state

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.