Can the small amount of money paid to the questioner be considered compensation for the increase he previously received due to an administrative error, if both errors were unintentional and from the same entity?

You have done well by informing the person in charge about the error, and it is not permissible for you to take payment for the days of absence. You should inquire about the reason for the deduction from the bonus. If the deduction is for the first error, then you are absolved. However, if it is for another error, and the amount of the increase you received is equal to what was deducted from you, and you were entitled to it, then there is no harm in waiving your right in exchange for what you owe through set-off. If the creditor's liability becomes occupied with the same type, description, and time of performance as what the debtor owes, then both liabilities are discharged by set-off without the need for reciprocal possession. Both debts are discharged if they are equal in amount; if they differ, the smaller amount is discharged from the larger, and the excess remains.