Hello @ArtOfSpring,
You do not need to run a Looper Consumer in an archive layout because the archive layout will just use the default WordPress loop. The pagination will only work if you do not have a Looper Provider in your archive layout.
Also, the pagination does not work with the Item number option in the Looper Consumer.

The pagination works with the total number of items set in Cornerstone > Theme Options > WooCommerce > Post per Page which the default value is 12.
This means that if in a particular category there are more than 10 items, you will expect to see the pagination at the bottom. If you only have less than 10 items, the pagination will not display.
In your Solar category archive, there are only 5 items. The first one is displayed as the hero item:
The rest of the 4 items will be displayed at the bottom. Now, if you want to enable the pagination, you will have to go to Cornerstone > Theme Options > WooCommerce > Post per Page and set it to 3
so that the pagination will display.
Hope this makes sense.