考虑到你想改变id=outer-section的元素的背景。
HTML：

<section id="outer-section">
    <section id="inner-section">
    </section>
</section>

JS：

document.getElementById("outer-section").style.background = "red"

// or using parentElement
document.getElementById("inner-section").parentElement.style.background = "red"

我不知道我是否理解正确，但你可以试试下面的代码。

const btn = document.getElementById('my-btn');
 const section = document.getElementById('my-section');
 const colors = ["red", "green", "blue"];
 const colorIndex = 0;
    
 btn.addEventListener('click', function() {
     const newColorIndex = parseInt((Math.random() * (3 - 1) + 1).toFixed());
     section.style.backgroundColor = colors[newColorIndex - 1];
 });

#my-section {
     height: 300px;
     border: 1px solid #000;
 }
        
 #my-btn {
     margin-bottom: 10px;
 }

<button id="my-btn">Click Me</button>
<div id="my-section"></div>