Admin Toolbar Extra Tools items on /admin/index

Here's an easier way to do this:

1). Copy admin-block.html.twig from core/modules/system/templates/admin-block.html.twig into your admin theme.
2). Add this twig:

{% set class = block.title %}
{% set class = class|replace({' ':''}) %}
{% set class = class|lower %}
{%
  set classes = [
    'panel',
     class,
  ]
%}

Then, the <code><div{{ attributes.addClass(classes) }}>

will include the class name of the region, in this case, admintoolbarsearch

Then, in your admin theme, just

div.admintoolbarsearch {
display:none;
}