What you want is to implement some object that stores your state, that can be modified using callback functions. You can then pass these functions to your React components.

For instance, you could create a store:

function Store(initialState = {}) {
  this.state = initialState;
}
Store.prototype.mergeState = function(partialState) {
  Object.assign(this.state, partialState);
};

var myStore = new Store();

ReactDOM.render(
  <FirstComponent mergeState={myStore.mergeState.bind(myStore)} />,
  firstElement
  );
ReactDOM.render(
  <SecondComponent mergeState={myStore.mergeState.bind(myStore)} />,
  secondElement
  );

Now, both the FirstComponent and SecondComponent instances can call this.props.mergeState({ . . .}) to assign state to the same store.

I leave Store.prototype.getState as an exercise for the reader.

Note that you can always pass the store (myStore) itself to the components; it just feels less react-y to do so.

Here is some more documentation that might be of interest:

React Docs: "Communicate Between Components"

For communication between two components that don't have a parent-child relationship, you can set up your own global event system. Subscribe to events in componentDidMount(), unsubscribe in componentWillUnmount(), and call setState() when you receive an event. Flux pattern is one of the possible ways to arrange this.

It is possible without any external state management library. Just use a simple observable implementation:

function makeObservable(target) {
  let listeners = []; // initial listeners can be passed an an argument aswell
  let value = target;

  function get() {
    return value;
  }

  function set(newValue) {
    if (value === newValue) return;
    value = newValue;
    listeners.forEach((l) => l(value));
  }

  function subscribe(listenerFunc) {
    listeners.push(listenerFunc);
    return () => unsubscribe(listenerFunc); // will be used inside React.useEffect
  }

  function unsubscribe(listenerFunc) {
    listeners = listeners.filter((l) => l !== listenerFunc);
  }

  return {
    get,
    set,
    subscribe,
  };
}

And then create a store and hook it to react by using subscribe in useEffect:

const userStore = makeObservable({ name: "user", count: 0 });

const useUser = () => {
  const [user, setUser] = React.useState(userStore.get());

  React.useEffect(() => {
    return userStore.subscribe(setUser);
  }, []);

  const actions = React.useMemo(() => {
    return {
      setName: (name) => userStore.set({ ...user, name }),
      incrementCount: () => userStore.set({ ...user, count: user.count + 1 }),
      decrementCount: () => userStore.set({ ...user, count: user.count - 1 }),
    }
  }, [user])

  return {
    state: user,
    actions
  }
}

And that should work. No need for React.Context or lifting state up