Klaviyo

Klaviyo does email and SMS marketing. It can integrate with a WooCommerce site through its plugin, also called klaviyo.

Plugin installation

wp plugin install klaviyo --activate

Klaviyo doesn't add any WP-CLI commands.

After establishing a Klaviyo account and installing their WordPress plugin, these two entities try to connect.

Klaviyo can't connect to a webshop where the plugin has been installed: Unable to access orders API

Some serious cashing happens at this site. Even the DNS entries point to somewhere else (CDN?). Maybe that's a problem?

Site » wp-admin » Plugins » Klaviyo » Setup: It asks for permission to exchange WooCommerce data. Nothing more. This permission originated on the website (so no issues with firewall). Also no issues concerning identificaiton of the Klaviyo account: That isn't even asked for (of course, Klaviyo knows which site connects to which account)
Uninstalled the plugin (which wasn't installed by me): wp plugin deactivate klaviyo; wp plugin uninstall klaviyo and reinstalled it: wp plugin install klaviyo --activate + run the procedure again: No difference
REST API is used for communications. This seems to work fine (see screenshot below)

Yep: Klaviyo uses REST API and credentials seem to have been established

Disable caching: Disabled Object Pro Cache (button dashboard) and WP Rocket (deactivated the plugin): No difference.