Try to add the below at the end of the templates.xml, this will show internal reference in shop page for all products and it will add toggle button in customize to active/inactive it:

<template id="products_item_internal_reference" inherit_id="website_sale.products_item" active="True"
          customize_show="True" name="Product Internal Reference">
    <xpath expr="//*[hasclass('product_price')]" position="before">
        <h6 class="o_wsale_products_item_title mb-1">
            <a class="text-primary text-decoration-none" itemprop="default_code" t-att-href="product_href"
               t-att-content="product.default_code" t-field="product.default_code"/>
        </h6>
    </xpath>
</template>
 

Note: Modify the Odoo module is not the best practice because if you update it to the latest revision, your added code will be removed so it's better to develop your custom module.