HTML page compiling LaTeX code to nice mathematics display - 2nd attempt
I'll just go through this as I find issues:


Don't declare your main dependency as async. In case the server goes down that makes your page look stupid. What you should do instead is check that the script was actually loaded before trying to use it.
JS standard naming convention for functions is camelCase. see the js-standard api as well as every major js framework. This is not python: get_url_parameter \$\rightarrow\$ getUrlParameter.
Same applies for variable names throughout your code. 
Use 'use strict' to force compliance to new JS standards. And use it in the largest scope you control alone:

function getUrlParameter(param) {
    'use strict'
    let pageUrl =  // ...

I like how you encapsulated the parameter getting into it's own method. I also like how you use standard functions to URI-encode correctly instead of rolling your own encoding
Last time I checked (which is a while ago) it was common to wrap top-level code into a self-executing function like this:

(function() {
    // ... 
})();


the main reason why is outlined here on SO
use let over var to communicate mutability intents to other developers (and the script engine). Also don't rely on implicit variable declaration. that's cheap :)
I never understood the point of aligning an assignment operation's right hand side :/
You can make things a tad easier when creating the encodedUrlTextarea.value by using template interpolation:

encodedUrlTextarea.value = `${location.protocol}//${location.host}${location.pathname}?code=${encodeURIComponent(latexInput.value)}`;


This can be made a bit cleaner with some extraction:

let baseUrl = `${location.protocol}//${location.host}${location.pathname}`;
let code = encodeURIComponent(latexInput.value);
encodedUrlTextarea.value = `${baseUrl}?code=${code}`;


As we can see, the creation of baseUrl can be pulled out of the function. It won't change during the script lifetime. Take advantage of that. It's definitely debatable whether the call to encodeURIComponent now really needs to be outside the template string