atillaordog

The search fields simply filter the lists in their current box.
Use the settings page to manage the location of search fields.
Simple as the sun, using easy JS.
Especially useful when there are a lot of categories, like in case of a shop.
It needs jQuery to run ! 
Trims beginning and ending spaces ! 
Works with the classic editor of WordPress 5, the new editor has this functionality included.

WP Admin Category Search

The plugin works flawlessly and is very simple.

Works fine and solved my problem

This plugin adds search functionality to category-like taxonomies and dropdowns like author on add / edit post / page admin pages.

Marios Alexandrou

DigitalME

As the name suggests this plugin will completely remove the mandatory ‘Category Base’ from your category permalinks ( e.g. ‘mysite.com/category/my-category/’ to ‘mysite.com/my-category/’ ).
The plugin requires no setup or modifying core wordpress files and will not break any links. It will also take care of redirecting your old category links to the new ones.
<h4>Features</h4>
<ol>
<li>Better and logical permalinks like ‘mysite.com/my-category/’ and ‘mysite.com/my-category/my-post/’.</li>
<li>Simple plugin – barely adds any overhead.</li>
<li>Works out of the box – no setup needed.</li>
<li>No need to modify WordPress files.</li>
<li>Doesn’t require other plugins to work.</li>
<li>Compatible with sitemap plugins.</li>
<li>Compatible with WPML.</li>
<li>Works with multiple sub-categories.</li>
<li>Works with WordPress Multisite.</li>
<li>Redirects old category permalinks to the new ones (301 redirect, good for SEO).</li>
</ol>

No Category Base (WPML)

This plugin removes the mandatory 'Category Base' from your category permalinks. It's compatible with WPML.

WP Admin Category Search vs No Category Base (WPML)