C&S is just a fulfillment warehouse and not buying anything. They handle the logistics and provide stock behind the scenes. What you’re seeing in what you linked is just them handling the “Store brands” for that particular chain.
Whomever the owners of the new chains are will have a choice of which warehouse they choice to do business with as there are a few larger players, but that depends on the region.
I worked IT for grocery for years and have had to deal with C&S as a middleman numerous times.