WooCommerce shortcode to output product categories randomly

functions.php

<?php
/**
 * Create the new WooCommerce shortcode [random_product_categories] to output product categories randomly.
 * Based on [product_categories] (/plugins/woocommerce/includes/class-wc-shortcodes.php).
 *
 * This new shortcode accepts all attributes used by [product_categories], except 'orderby' and 'order', of course.
 * See more at @link https://woocommerce.com/document/woocommerce-shortcodes/.
 *
 * @param  array $atts User defined attributes in shortcode tag.
 */
function random_product_categories_shortcode( $atts ) {
	global $woocommerce_loop;

	$atts = shortcode_atts( [
		'number'     => null,
		'columns'    => '4',
		'hide_empty' => 1,
		'parent'     => '',
		'ids'        => '',
		'hide_title' => 0,
	], $atts );

	if ( isset( $atts['ids'] ) ) {
		$ids = explode( ',', $atts['ids'] );
		$ids = array_map( 'trim', $ids );
	} else {
		$ids = [];
	}

	$hide_empty = (bool) $atts['hide_empty'];

	// Get terms and workaround WP bug with parents/pad counts.
	$args = [
		'hide_empty' => $hide_empty,
		'include'    => $ids,
		'pad_counts' => true,
		'child_of'   => $atts['parent']
	];

	$product_categories = get_terms( 'product_cat', $args );

	// Shuffle the array of objects `$product_categories`.
	shuffle( $product_categories );

	if ( '' !== $atts['parent'] ) {
		$product_categories = wp_list_filter( $product_categories, [ 'parent' => $atts['parent'] ] );
	}

	if ( $hide_empty ) {
		foreach ( $product_categories as $key => $category ) {
			if ( $category->count == 0 ) {
				unset( $product_categories[ $key ] );
			}
		}
	}

	if ( $atts['number'] ) {
		$product_categories = array_slice( $product_categories, 0, $atts['number'] );
	}

	$columns                     = absint( $atts['columns'] );
	$woocommerce_loop['columns'] = $columns;

	ob_start();

	// Reset loop/columns globals when starting a new loop.
	$woocommerce_loop['loop'] = $woocommerce_loop['column'] = '';

	if ( $product_categories ) {
		woocommerce_product_loop_start();

		if ( ! empty( $atts['hide_title'] ) ) {
			remove_action( 'woocommerce_shop_loop_subcategory_title', 'woocommerce_template_loop_category_title' );
		}

		foreach ( $product_categories as $category ) {
			wc_get_template( 'content-product-cat.php', [
				'category' => $category
			] );
		}

		if ( ! empty( $atts['hide_title'] ) ) {
			add_action( 'woocommerce_shop_loop_subcategory_title', 'woocommerce_template_loop_category_title' );
		}

		woocommerce_product_loop_end();
	}

	wc_reset_loop();

	return '<div class="woocommerce columns-' . $columns . '">' . ob_get_clean() . '</div>';
}

add_shortcode( 'random_product_categories', 'random_product_categories_shortcode' );

@Hebhansen It seems the cache comes from Cloudflare. You'd have to correctly setup your cache settings under the Cloudflare platform and/or under any WP plugin that integrates your website with Cloudflare.

About the overflow I couldn't reproduce what you described.