You can get the total category count for the store in Magento 2 by using the getCount() method.

You can fetch that information from
MagentoCatalogApiCategoryManagementInterface.

All you need to do is just create a simple Model class which will help you to retrieve the total number of the category.  Code is as per below.

<?php
namespace MagemonkeyCategoryCountModel;
 
use MagentoCatalogApiCategoryManagementInterface;
 
class CategoryCount
{
    /**
     * @var CategoryManagementInterface
     */
    private $categoryManagement;
 
    public function __construct(
        CategoryManagementInterface $categoryManagement
    ) {
        $this->categoryManagement = $categoryManagement;
    }
 
    /**
     * Fetch all Category count
     *
     * @return int
     */
    public function getCategoryCount()
    {
        $categoryCount = $this->categoryManagement->getCount();
 
        return $categoryCount;
    }
}

Once you done with the code part, you can call method by using below command,

$categoryCount = $this->getCategoryCount();

That’s it.