Hello @Luke Adams,
Welcome to the Klaviyo Community!
Since the error message you highlighted is pointing to an authorization error, I would first recommend ensuring that the user assigned in the REST API was set to Admin with Read/Write permissions. Another common issue that may cause this error is if you happen to have a firewall that may be prevent Klaviyo from initiating this sync. This can be resolved by listing “Klaviyo/1.0” as an acceptable user-agent for all requests to avoid this firewall issue.
Lastly, I would also recommend ensuring that you are on the most up to date plugin/extension version. At this time, the most up to date Klaviyo plugin version is 2.4.1. You can download the latest Klaviyo WooCommerce plugin version manually from the Wordpress store.
All of these points I mentioned are also elaborated further the below Community posts which touch upon this subject of receiving an integration error:
Hope this helps!
David