What is the ruling on personal financing from Qatar Islamic Bank (QIB), in which the bank buys a commodity then sells it to the client, then buys it back at a lower price based on authorization from the client?

The described scenario—if the bank buys the commodity back from the client—is impermissible because it falls under the prohibited 'inah (buy-back) transaction. This occurs when one sells a commodity for a known price on credit, then buys it back from the same person for a lesser price, leaving a larger amount as a debt upon him. You can refer to the Sharia Supervisory Board of the mentioned bank and inquire from them about the true nature of the transaction.