Custom admin/user icons in header

That looks like a CSS issue. Easier to debug when looking at the site in a browser with the inspector open.

I didn’t look at the first script at all earlier, because I didn’t see an icon reference, but, in fact, you should merge the two scripts together to something like this:

<script type="text/discourse-plugin" version="0.8">
const { iconNode } = require("discourse-common/lib/icon-library");
let currentUser = api.getCurrentUser();
let icon = 'admin-icon';
if (currentUser && !currentUser.admin) {
  icon = 'shopping-cart';
}
api.decorateWidget('header-icons:before', helper => {
return helper.h('li', [
    helper.h('a#home-button', {
        href:'https://Example2.com',
        title: 'Button 2'
    }, iconNode(icon)),
]);
});
}
</script>

This will use admin-icon for admins and shopping-cart for non-admins. (Use an icon of your choice instead of the admin-icon placeholder I put in the code above.)