I create a web component with this code where I use template:
let tmpl = document.createElement('template');
tmpl.innerHTML =`<style>
div {
color: green;
display: inline;
margin: 3px;
}
p {
border: 1px solid black;
}
</style>
<p>
Hello my name is:
<div>Web</div>
<div>Component</div>
</p>`;
this.shadowRoot.appendChild(tmpl.content.cloneNode(true));
But in shadow root from console I see this content which not the same:

It has nothing to do with Shadow DOM or Custom Element.
Actually the same behaviour happens with normal DOM : you cannot insert a
<div>element inside a<p>element. The latter only accepts phrasing content.See SO question: Why
<p>tag can't contain<div>tag inside it?