This might work for you (but requires advanced UI based customization of Odoo):

Create a new field on the Product model (in this case the Product Variant):

Use Odoo Studio to add a new BUTTON to the Product Form View:

Relate the BUTTON to the field you created:

You will see the new BUTTON on the UI:

Click the BUTTON to edit the LIST VIEW on that screen:

What you want is an inherited view that allows you to CREATE documents (ie: upload them from the List):

Once you refresh the screen, you will see the CREATE button on the list and you can associate your files with the Product that way.

Then you probably also want to edit the Window Action to allow the familiar KANBAN view to be shown:

You will end up with this:

Note that you want to prevent CREATE from the Kanban (on this Window Action only) because if you don't, the Document won't be associated properly to the Product.   Perhaps with more time, I could figure out how to resolve that (or if you are reading and YOU can solve that last piece, please edit my answer)