For a D visa you need a policy for the whole visa period with cover from 30,000 euro, and since 2024 the questura asks for insurance with the kit too. Travel policies for 700-4,500 roubles lose validity after 90 days in the country; for the first year people buy an annual private policy (about 500 euro a year was quoted in the chats) or pay to join the SSN.
SSN registration does not lapse during a renewal (art. 42 c. 4 DPR 394/1999): take the ricevuta to your ASL, which extends it and issues a temporary card.