Here's how to handle it with WooCommerce
For every integration that you want to do, you can get a unique API key where you specify the permissions. (read / read/write)
What I mean by that is - for every instance of usage of a WooCommerce instance (such as integration between WooCommerce and AI or whatever) you generate a new unique key that you can define read/write access on.
Let me explain with some example use cases:
Use Case 1: Your AI tool wants access to your products database to show it to users, create or update products.
What you do - you generate a read/write key for that one integration.
Use Case 2: Your AI tool wants to know about what products are available (and maybe what's been sold or whatever you decide) - create a read-only key
One thing you absolutely 100% do not want to do - specify the actual owner account to your WooCommerce. That will always be your actual user. Never do that!
Does your tool actually need to write anything or just read??