Is it permissible to use a portion of a client's money, which was given to be deposited into a savings account at an Islamic bank, with the intention of compensating the owner with the due profit percentage on the amount used when profits are distributed, knowing that the owner of the money is unaware of this, and is this act considered usury (riba)?

You erred by taking the money without the owner's knowledge, because it was a trust, and your taking it makes you liable for it. Therefore, you must return an equivalent amount. If you profited from it, the profit belongs to the owner of the money, and you should inform him to agree on its distribution. If you did not profit, then only return an equivalent amount, and it is permissible to add more as a gift. You must repent and feel remorse, resolve not to repeat the action, inform the owner of the money, and seek his forgiveness, unless you fear a greater harm, in which case you should only return the money.