We would like to automatically assign the Path Alias for each new Product as /products/sku.
How can we do this, either from the URL Alias admin UI or via Rule or programmatically?
Pathauto should give you enough flexibility to do that.
Once your "product" content type has a
commerce_product_reference field linked to it (let's call it "field_product"), all fields attached to your "product variation type" should be available as tokens like this:
[node:field-product:product-id] or if you created a specific field to store the value
You probably know it but patterns can be configured from here :