What is the ruling on dealing with a bank that stipulates providing 20% of the purchase price and depositing it therein, then deposits the remaining amount after its approval and grants a power of attorney to purchase in the bank's name, so that it becomes owned by the bank and then sold to the client?

The permissible Murabaha sale requires the bank to first purchase the goods for itself, so they enter into its possession and responsibility. Then, it sells them to the customer. The bank's condition of requiring an upfront payment of a portion of the price, or authorizing the customer to pay the price and receive the goods, does not affect this. The transaction mentioned in the question does not seem to fulfill these conditions. Therefore, it is more prudent to abstain from it until its execution aligns with Islamic law.