What Amazon is typically accused of, having store brands, is what every retailer does. That's hard to win. Maybe there are other things, but I haven't heard of them.
This is simply not true and displays a fundamental misunderstanding of how retail works. A retailer pays the supplier for the stock of inventory that goes on its shelves, Amazon does not. (It is only in very rare cases the supplier only gets paid for actual sales of retail inventory; generally this happens for new products offered on a consignment basis to demonstrate market demand.) Frequently, retailers will share sales data with their suppliers so that the suppliers can make more attractive products, because then they can sell more units to end customers or charge higher markups.
But importantly, with retail, the retailer is the supplier's customer, not you.
In contrast, Amazon does not buy the inventory from the suppliers, instead it charges them money to store their inventory in Amazon's warehouses. On top of that, Amazon uses its access to sales data of external suppliers' products to design competing products which it then offers for sale, utilizing its ownership of the platform to promote its own products above competing products. While both of these latter two activities are problematic, it is the last one that definitely runs afoul of antitrust law (and was what got Microsoft into trouble with the EU).
The problem with Amazon: it is using its position as the controller of the dominant online marketplace to establish a position in the market for individual categories of goods in a manner that interferes with the normal dynamics of the market.
That part seems entirely reasonable. Would you rather Amazon pay sellers for unsold stock? That seems like a sure way to get Amazon to reduce the number of 3rd party sellers they stock.
From personal experience so, once Amazon loses the buy box, the measures to gain it back are more or less what other seller could do as well. No idea how much seller data they use in selecting private brand products so.
All the retailers have data on what sells in their store, they also have the data on how sales are influenced by shelf placement.
Amazon to me is a logistics company, along with their storefront and AWS. Their focus on margins and their competence to use data to drive their logistics chains is what's truly scary. They can optimize a lot of inefficiencies that exist in logistics right now just because of the involvement of different disjoint players.
Hoe all that translates into anti-trust law, I have no idea.
Should we define a line between marketplace operators and marketplace competitors? Or at least define rules to better ensure fair competition?