Is it permissible for the owner of a commercial company or a supermarket to offer a customer of another company to buy from him at a lower price, and is this considered selling over the selling of his Muslim brother?

It appears that this situation does not fall under the prohibition of a Muslim selling over his Muslim brother's sale, due to the absence of any sale or bidding to begin with, let alone the inclination and rapprochement between the buyer and the seller. The prohibition of bidding is conditioned on the seller's inclination towards the buyer and their rapprochement, such that each of them is inclined to buy and sell, and all that remains is the verbal offer and acceptance. Imam Malik, in Al-Muwatta, explained the prohibition of "some of you selling over the sale of others" as bidding over a brother's bid when the seller has inclined towards the bidder, and this is evident by the stipulations and the complete agreement between the two parties.