Is it permissible for a person overseeing the finishing of an apartment to keep the price difference resulting from discounts he obtains from suppliers or craftsmen, without the apartment owner's knowledge, especially since he does not receive a wage for his oversight?

It is not permissible for an agent to take anything except with the knowledge of his principal. All rights of the contract revert to the principal, not to the agent. Even if the seller gives a gift to the agent, it belongs to the principal, serving as a reduction in the price.