href link not working with innerHTML script with "onmouseover change text" and onmouseout

My goal is to have text change onmouseover from "hello" (without a link) to "Google" and provide an 'href' on the resulting "Google" text, and then revert to "hello" onmouseout without a link.

The code below works in changing the text from "hello" to "Google" but,

1. the link on "Google" does not work (even though I can right-click on "Google" and open the link on another tab)

2. the text does not change back to "hello" onmouseout.

Thanks for your help in advance!

Here is my code:

<style>
    .container {
        margin-top: 6vw;
        margin-left: 40%;
        margin-right: 40%;
}
</style>

<div class="container">
    <h1>
        <div class="hello" id="hello1" onmouseover="changeText()" onmouseout="changeText(this,'Hello.')">Hello.</div>
    </h1>
</div>

<script>
    function changeText() {
        if (document.getElementById("hello1")) {
            a = document.getElementById("hello1")
            a.innerHTML = '<a href="https://www.google.com">Google</a>'
        }
    }
</script>

By changing a class of a parent tag, any and all child tags can be affected via CSS. Having the HTML ready when the page loads and then hiding it is better than constantly creating and destroying HTML for trivial effects.

The events "mouseenter" and "mouselrave" are handled by a property event handler and an event listener. Either one is sufficient, but avoid using attribute event handlers:

 <div onmouselame="lameAttributeEventHandler()">...</div>

Details are commented in the example below

// Reference the <header>
const hdr = document.querySelector('.title');

/* This is a property event handler
// Whenever the mouse enters within the borders of
// the <header>:
//            '.google' class is added
//            '.hello' class is removed
*/
hdr.onmouseenter = function(event) {
  this.classList.add('google');
  this.classList.remove('hello');
};

/* This is an even listener 
// Whenever the mouse exits the <header> the
// opposite behavior of the previous handler 
// happens
*/
hdr.addEventListener("mouseleave", function(event) {
  this.classList.add('hello');
  this.classList.remove('google');
});

.title {
  height: 50px;
  margin-top: 3vh;
  border: 3px solid black;
  text-align: center;
}

h1 {
  margin: auto 0;
}

.hello span {
  display: inline-block;
}

.hello a {
  display: none;
}

.google a {
  display: inline-block;
}

.google span {
  display: none;
}

<header class="title hello">
  <h1>
    <span>Hello</span>
    <a href="https://www.google.com">Google</a>
  </h1>
</header>