Taxonomy is not a blog

Help please, my head broke already. I have a few projects in the site. Displayed on a '/sites' in a list. Each project has its own category: 'categorysites', in the head of the module page with categories and has the approximate form:

{% set categories = taxonomy.taxonomy['categorysite'] %}
  <div class="tags">{{ page.title }}:</div>
      {% for categorysite, items in categories %}
        <a class="link-category-sites" href="{{ page.parent.url }}/category{{ config.system.param_sep }},{{ categorysite }}">{{ categorysite }} (<span>{{ items|length }}</span>)</a>
      {% endfor %}

The names of the categories, the number in parentheses, it works, but when you click on a link, display the selected category does not take place, all projects are displayed initially. What could be the problem?
Taxonomy in a blog on this site works fine.
Sorry for my english, I hope everything is clear.
Thank

I can even use taxonomy not only for the blog on the same site?

If the taxonomy is named categorysite, then the URL must be /categorysite:something, you have /category:something now.

This non-playing no role. Can anyone give an example of a taxonomy for the blog and for projects such as taxonomy on one site? How to implement this? I do the same as for a blog, but it does not work.

Sorry, but I have made a mistake, and it works. The mistake was that the template with a list of projects I used the code:

{% for p in page.find('/projects').children %}
{% include 'partials/project_item.html.twig' %}
{% endfor %}

Because of this, I obtained a list of projects and taxonomy was not working.
And it was necessary to:

{% for p in page.collection %}
{% include 'partials/project_item.html.twig' %}
{% endfor %}

Ok :)