We can achieve the requirement to adding the newsletter signup popup script from the klaviyo ESP account to the WC site. To achieve this requirement we need to install a Klaviyo plugin on the WC website.
After the installation of the plugin, we need to connect the Klavio account with the WC website by setting up the Public key / SiteID.
The detailed document on Klviyo integration with WC is available on mentioned document. Please find
https://help.klaviyo.com/hc/en-us/articles/115005255808-How-to-Integrate-with-WooCommerce
Thank you.