Is the split year residence relief applicable to your situation?
This page gives details of what split-year treatment is and how to apply
Employment income (and only employment income) earned outside the State in the year you become tax resident (2022) up to the date of arrival falls outside the charge to tax, providing you will be tax resident in Ireland in the following year (2023).
If the bonus was paid in February 2022 and you arrived 1 Mar 2022, then even though you are tax resident for 2022, this income is outside the charge to tax. Not sure of the sequencing of your arrival, bonus payment though.
If this relief isn't applicable, it's looking like it is an emolument and subject to Irish tax under Schedule E but I'm not qualified to advise in this area.