Is it permissible to take the interest that the bank gives on deposited money at a certain rate without request, given that the source of this money is unknown, whether it is permissible or forbidden?

The benefits granted by a riba-based bank on a deposit are considered usury (riba), because a deposit in a riba-based bank is a loan that is returned with an increase.

The depositor must withdraw the deposit immediately and dispose of the interest by spending it on charitable causes, public benefits for Muslims, or on the poor and needy.

If the depositor was unaware of the prohibition of these benefits, then he does not incur sin by depositing, but he must spend the interest on charitable causes and it is not permissible for him to own it.