What do I need to be able to move to my home in Calabria

If you are an Italian citizen then you dont need a visa or PdS.  You will probably have to take out a health insurance if you havent paid tax in ITaly for the last 5 years, but they will tell you at the ASL or the anagrafe when you go to register.

Thank you for such a quick response.  I have heard of Americans with dual citizenship, are being able to go to and fro!  I guess I'd have to self quarantine. At customs do I just show my American passport, and my carte de identita?  Can I have a friend purchase the medical insurance for me since I will be in self quarantine?  I have had both Phizer shots, will I need to show a negative Covid test?. Also I will have my pet dog with me!

Theres a big difference between now and 'by the end of the year'.   I wouldnt try to go anywhere for another 3 months.   As an Italian citizen you laways have the right to return toyour place of residence, so it depends if your property in Calabria is your residence or not.   
A friend cannot buy your medical insurance - its only 2 weeks of self quarantine, and then you can start the 'immigration game'.

If you take a covid teste flight, you won’t need to quarantine. I came from USA in December and I took that flight. No issues at all.