For using SSO with WP Discourse and Woocommerce, you may need to add this plugin to your site: GitHub - scossar/wp-discourse-woocommerce-support: Integrates the wp-discourse plugin with WooCommerce · GitHub.
The plugin’s README explains what it’s doing. Instead of installing the wp-discourse-woocommerce-support plugin, you can copy the code from the README’s ‘Alternatives to installing the plugin’ section into your theme’s functions.php file.