LevelCalculator.php

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<?php
declare(strict_types=1);

namespace Magento\CatalogGraphQl\Model\Category;

use Magento\Framework\App\ResourceConnection;
use Magento\Catalog\Model\ResourceModel\Category;

class LevelCalculator
{
    public function __construct(
        ResourceConnection $resourceConnection,
        Category $resourceCategory
    ) {
        $this->resourceConnection = $resourceConnection;
        $this->resourceCategory = $resourceCategory;
    }

    public function calculate(int $rootCategoryId) : int
    {
        $connection = $this->resourceConnection->getConnection();
        $select = $connection->select()
            ->from($this->resourceConnection->getTableName('catalog_category_entity'), 'level')
            ->where($this->resourceCategory->getLinkField() . " = ?", $rootCategoryId);
        return (int) $connection->fetchOne($select);
    }
}