So basically you need to have onMouseEnter and onMouseLeave on parent elements and make a state that holds whether to show the additional data here is a simple example

import "./styles.css";
import {useState} from 'react'

function Children(){
  return (
    <>
        <img src='https://picsum.photos/200/300' />
        <p>details  of header</p>
        <button>add to favorite</button>
    </>
  )
}

function Parent() {
  const [isMouseOver,setIsMouseOver] = useState(false)

  const handleEnter = () => {
    setIsMouseOver(true)
  }

  const handleLeave = () => {
    setIsMouseOver(false)
  }
  return(
    <div onMouseEnter={handleEnter} onMouseLeave={handleLeave}>
      <h1>Hover me</h1>
      {isMouseOver ?
      <>
        <Children />
      </>:
      null
      
    }
    </div>
  )
}

export default function App() {
  return (
    <div className="App">
      <Parent />
    </div>
  );
}

Similarly, you would change the Parent component to your li and the additional data that should be visible to Children Component.

Note that in this example h1 is a block component so you should leave the whole block to make the data disappear

demo at : https://codesandbox.io/s/silly-dewdney-d8btf?file=/src/App.js:0-738

You can add some class and in its respective CSS, handle the mouseover (:hover).

App.js

import "./styles.css";

function ListItem({i})
{
  return (
    <li className="listitem">
      <a href="stackoverflow.com">Link{i}</a>
      <img className="hideele" src="" alt={i} />
      <p className="hideele">Para{i}</p>
      <button className="hideele">Button{i}</button>
    </li>
  );
}

export default function App() {
  return (
    <div className="App">
      <ul>
        <ListItem i={1} />
        <ListItem i={2} />
        <ListItem i={3} />
      </ul>
    </div>
  );
}

Index.js

import { StrictMode } from "react";
import ReactDOM from "react-dom";

import App from "./App";

const rootElement = document.getElementById("root");
ReactDOM.render(
  <StrictMode>
    <App />
  </StrictMode>,
  rootElement
);

CSS:

.App {
  font-family: sans-serif;
}
.listitem:hover .hideele {
  display: block;
}
.hideele {
  display: none;
}