This is my code enter image description here
<script>
let myDiv = document.createElement("div");
myDiv.classList.add('test');
let my_var = `<?php echo do_shortcode("[elementor-template id="5078"]"); ?>`;
myDiv.innerHTML = my_var;
document.querySelector("#instagram").appendChild(myDiv);
</script>Actually, it is not possible to do it this way because the script is being fired on the client-side while the PHP interpreter is working on the server-side. If you are sure that you need to use JS to render some PHP code, I'd suggest sending a request using wp_ajax https://codex.wordpress.org/AJAX_in_Plugins to send a request on a server, and then the server can return any PHP code result that you want. Don't forget that shortcodes may use additional assets that will not be sent as a response.
The best way is to use shortcodes in a native form inside the content or PHP templates. Especially the elementor template where you can create template parts for different places of the website easily.
It's an enclosure problem:
You used nested double quotes in your php – resulting in breaking the echo.
Provided, your <script> tag is in your template php (so your php shortcode could be parsed) try this (replace the shortcode double quotes by single quotes):
<script>
let myDiv = document.createElement("div");
myDiv.classList.add('test');
let my_var = `<?php echo do_shortcode("[elementor-template id='5078']"); ?>`;
myDiv.innerHTML = my_var;
document.querySelector("#instagram").appendChild(myDiv);
</script>