Is buying the shop after the expiration of its lease contract, with the tenant intending to buy the shop despite his previous breaches of appointment, considered buying over the buying of a Muslim? And what is the correct Islamic course of action for dealing with this stubborn tenant?

It is forbidden to sell over a brother’s sale or to buy over his purchase. This includes bidding, such as when a buyer and seller agree on a price, then another person comes and offers a higher price. The prohibition covers the period of option (khiyar) and after the completion of the contract, as it may lead to regret or resentment. However, in this case, the sale has not yet been completed, and the buyer is considered to have withdrawn, so there is no harm for you in buying the shop. As for the other person’s attempt to buy the shop after you have bought it, this is forbidden and falls under "buying over his brother’s purchase."