Add class whenever a WordPress category is displayed

On my Wordpress Elementor blog, there are several places where categories are listed. For example below on a blog post page:

<span class="elementor-post-info__terms-list">
    <a href="https://website.nl/culture/" class="elementor-post-info__terms-list-item">Culture</a>
</span>

I'd like to use CSS to style each category with a specific color.

For that, I need to either have the ID added as a class, or display a custom field I have created using ACF. Doesn't matter to me, but I can't figure out how to add a filter/action to add a custom class or a connected ACF paramter whenever a category is displayed on my website.

You can just use a CSS Attribute selector for this:

a[href*="culture"] {
    color: purple;
}

[href*="culture"] - selects an a tag where the href attribute contains "culture"

Since you'll know the term name, you can just build out your CSS for each one. No reason to add a class or hack the term list Elementor widget.

a[href*="culture"] {
  color: purple;
  font-size: 20px;
}

a[href*="another"] {
  color: blue;
  font-size: 14px;
}

<span class="elementor-post-info__terms-list">
    <a href="https://website.nl/culture/" class="elementor-post-info__terms-list-item">Culture</a>
    <a href="https://website.nl/another/" class="elementor-post-info__terms-list-item">Another</a>
</span>