As Laurel correctly pointed out, if you reside in Italy 183 days in a calendar year or longer, you are subject to Italian Income tax.
There is a bilateral tax treaty between the US and Italy, therefore you won't be subject to double taxation.
The US requires US citizens residing abroad to file income taxes, even though many may not owe any US taxes.
This is the way it works for Non Italian citizens (as I presume you do not hold Italian citizenship otherwise you wouldn't need an elective residency visa).
Public Pensions (i.e. Social Security benefits) will be taxed by the US government but NOT from Italy (if you were Italian, they would be taxed by Italy).
Private Pensions will be taxed by the Italian government according to the income bracket (but they are not taxed by the US gov't).
Income tax brackets in Italy are high, and hit incomes at comparatively low levels compared to the US. These are the brackets for 2021 and apply individually (therefore separately for husband and wife if both earn income).
Euro 75,001 and above=43%
In addition to the above there is an additional local tax to be added, which varies according to municipality, but it's small.
Interest, dividends, short term capital gains are all taxed at a flat rate of 26% (In the US they are added to your income and pay according to your bracket.
Long term capital gains are taxed also at the same flat rate of 26% (in the US they are taxed at 15 or 20%, depending on total income)
There are some expenses that can be detracted from income tax (for example medical expenses) but there is no Standard Deduction like in the US.
There is also an asset tax for assets held overseas, they are called IVIE and IVAFE.
The former (IVIE) is a property tax on real estate held in a foreign country. It is equal to 0,76% of the value of the property calculated based on the price of acquisition. From this tax it is however possible to deduct the property tax you pay to the locality where the property is located. I don't know the details of how much one can deduct but it is possible that it won't amount to much since property taxes in the US, which could be deducted from the amount owed to Italy, are generally higher than 0.76% of the purchase price.
The latter tax (IVAFE) is a wealth tax on the value of financial assets other than real estate (savings accounts, checking accounts, mutual funds, stocks, bonds, IRA etc.). It is equal to 0,2% of the value of the assets. So it's about $2000 for every million in assets.
So a couple receiving $3000 a month each in private pensions ($36000 each a year) should expect to pay at least $15000 more in income taxes per year compared to the US (assuming living in a US State with no income taxes). To that add $2000 for every million held in assets.
In spite of paying so much in extra taxes that is still not enough to get you cover by the Italian National Health Service. You will need private health insurance for that, or you can buy into the Italian NHS by paying a flat amount per year. That amount is based on your income, based on this formula:
Income in Euro:
Therefore if your income is euro 51645.69 or anything above, you will pay the maximum which amounts to Euro 2,789 per year, or about $270 a month (not too bad compared to an ACA insurance plan in the US)