Is the described banking transaction, which involves the bank buying shares and selling them to the client on a deferred basis, then the client immediately selling them to a third party, considered legitimate or usurious? And what should the client do if it is usurious?

There is no objection to the transaction if the bank is not committed to arranging the sale of shares to you directly or through a broker, as long as the bank has acquired ownership of the shares and then sold them to you after they entered its possession and guarantee. It does not matter that you specified shares of a particular company, or that the buying and selling took place on the same day via phone or internet, or that you authorized the bank to act as a broker on its behalf in buying and selling the shares to you, or that you authorized the same broker to sell them to you in the market. The fundamental principle regarding sales is permissibility unless an exception is established by evidence, as in the Almighty’s saying: "And Allah has permitted trade and forbidden interest."