Вы имеете в виду это? Вставить div перед заголовком?
let newDiv = document.createElement('div');
newDiv.className = 'Hello';
newDiv.id = 'Hello Id';
newDiv.setAttribute('tile', 'This Is Test');
let chNode = document.createTextNode('Something is Here');
newDiv.appendChild(chNode)
newDiv.style.background = 'red';
newDiv.style.padding = '2%';
let container = document.querySelector('header > .container')
let headh1 = container.querySelector('h1');
console.log(headh1)
headh1.closest("div").insertBefore(newDiv, headh1)
<header id="main-header" class="bg-success text-white p-4 mb-3">
<div class="container">
<div class="row">
<div class="col-md-6">
<h1 id="header-title">Item Lister</h1>
</div>
<div class="col-md-6 align-self-center">
<input type="text" class="form-control" id="filter" placeholder="Search Items...">
</div>
</div>
</div>
</header>
Или перед строкой?
let newDiv = document.createElement('div');
newDiv.className = 'Hello';
newDiv.id = 'Hello Id';
newDiv.setAttribute('tile', 'This Is Test');
let chNode = document.createTextNode('Something is Here');
newDiv.appendChild(chNode)
newDiv.style.background = 'red';
newDiv.style.padding = '2%';
let container = document.querySelector('header > .container')
let headh1 = container.querySelector('h1');
let row = headh1.closest(".row")
container.insertBefore(newDiv, row)
<header id="main-header" class="bg-success text-white p-4 mb-3">
<div class="container">
<div class="row">
<div class="col-md-6">
<h1 id="header-title">Item Lister</h1>
</div>
<div class="col-md-6 align-self-center">
<input type="text" class="form-control" id="filter" placeholder="Search Items...">
</div>
</div>
</div>
</header>