I'm unsure why I can't do a vector search based on my current ids I gather myself?

Instead of having product names, you can also just have product IDs that a user has interacted with. One user per row. E.g.

nmoiadoijad alkdADW97
abcdef1 abcdef2

The guide does mention that this format is allowed, quoting the docs:

TIP

We're using the

product_name

in this example to make this article easier to read. In a production setting, you'd want to use the product's ID or SKU in the training dataset