Solicitation, effectuation or delivery of any insurance contract, by mail or otherwise, within this State by an unauthorized insurer, or the performance within this State of any other service or transaction connected with such insurance by or on behalf of such insurer, is deemed to constitute an appointment by such insurer of the superintendent and the superintendent’s successors in office as its attorney, upon whom may be served all lawful process issued within this State in any action or proceeding against such insurer arising out of any such contract or transaction; and is deemed to signify the insurer’s agreement that any such service of process has the same legal effect and validity as personal service of process upon it in this State. [RR 2021, c. 1, Pt. B, §202 (COR).]