When creating a child theme, if your parent theme includes styles for WooCommerce navigation which you prefer, here’s a simple way to match the look and markup of the nav on non-WooCommerce pages, so you don’t have to rewrite the styles for it.

In your template files, update the_posts_pagination() (or replace your parent theme’s custom pagination function) to match the default settings found inside WooCommerce. For example, inside search.php:

the_posts_pagination(
	array(
		// match WooCommerce settings
		'prev_text' => '←',
		'next_text' => '→',
		'type'      => 'list',
		'end_size'  => 3,
		'mid_size'  => 3,
	)
);

In your functions.php file, update the HTML output of the navigation using the navigation_markup_template filter.

Check your parent theme’s style rules to see how specific they get. In my case, my parent theme specifies .woocommerce nav.woocommerce-pagination ul, so I will need to add a container with the .woocommerce class and add the .woocommerce-pagination class to our nav element. I also need to remove the .nav-links container so some other style rules match:

function wpdocs_pagination_output( $template, $class ) {
	
	$template = '
	<div class="woocommerce">
		<nav class="woocommerce-pagination navigation %1$s" role="navigation" aria-label="%4$s">
			<h2 class="screen-reader-text">%2$s</h2>
			%3$s
		</nav>
	</div>';

	return $template;
}
add_filter( 'navigation_markup_template', 'wpdocs_pagination_output', 99, 2 );

Note: 99 is the arbitrary priority I’ve assigned to the filter. Use a high number to run your filter last.