Override for mod_menu with the count of articles for each category. Put it to /templates/{your_template}/html/mod_menu/default_component.php. Tested on Joomla 3.

default_component.php

<?php
/**
 * @package     Joomla.Site
 * @subpackage  mod_menu
 *
 * @copyright   Copyright (C) 2005 - 2020 Open Source Matters, Inc. All rights reserved.
 * @license     GNU General Public License version 2 or later; see LICENSE.txt
 */

defined('_JEXEC') or die;

use Joomla\CMS\Categories\Categories;

// Initialize our output.
$itemsCount = '';

// If this menu item is for com_content.category, lets count articles in it.
if ($item->query['option']=='com_content' 
	&& $item->query['view']=='category')
{
	// Get Categories instance with the option to count items in it.
	$categories = Categories::getInstance('Content', ['countItems' => 1]);
	$numItems   = $categories->get($item->query['id'])->numitems;

	// Style for our output.
	if ($numItems > 0)
	{
		$itemsCount = ' <span class="articles-count">(' . $numItems . ')</span>';
	}
}

$attributes = array();

if ($item->anchor_title)
{
	$attributes['title'] = $item->anchor_title;
}

if ($item->anchor_css)
{
	$attributes['class'] = $item->anchor_css;
}

if ($item->anchor_rel)
{
	$attributes['rel'] = $item->anchor_rel;
}

$linktype = $item->title;

if ($item->menu_image)
{
	if ($item->menu_image_css)
	{
		$image_attributes['class'] = $item->menu_image_css;
		$linktype = JHtml::_('image', $item->menu_image, $item->title, $image_attributes);
	}
	else
	{
		$linktype = JHtml::_('image', $item->menu_image, $item->title);
	}

	if ($item->params->get('menu_text', 1))
	{
		$linktype .= '<span class="image-title">' . $item->title . '</span>';
	}
}

if ($item->browserNav == 1)
{
	$attributes['target'] = '_blank';
}
elseif ($item->browserNav == 2)
{
	$options = 'toolbar=no,location=no,status=no,menubar=no,scrollbars=yes,resizable=yes';

	$attributes['onclick'] = "window.open(this.href, 'targetWindow', '" . $options . "'); return false;";
}

// Add articles count to link text.
$linktype .= $itemsCount;

echo JHtml::_('link', JFilterOutput::ampReplace(htmlspecialchars($item->flink, ENT_COMPAT, 'UTF-8', false)), $linktype, $attributes);