To the extent permitted by federal law, each state agency that is a party to a Probate Court proceeding shall recognize and apply any order, denial or decree of a Probate Court, issued on or after October 1, 2022, provided such Probate Court has statutory jurisdiction to issue such order, denial or decree. Any party aggrieved by such order, denial or decree of such Probate Court may appeal therefrom to the Superior Court in accordance with § 45a-186. As used in this section, “state agency” means an agency, as defined in § 4-166.