Momof3 - United flight 40 from EWR to JFK is covid tested. Their website is confusing. It doesn't say which flights are covid tested but this page on their website says "United’s flights from New York/Newark to Milan and Rome are COVID-tested flights."
https://www.united.com/ual/en/us/fly/travel/notices.html#europe-waivers
I booked UA Flight 40 today. Because the website wasn't clear, I called their customer service first and the rep was clueless so I reached out to them via private message on twitter. They confirmed that it is a covid tested flight so I booked. After I booked, I checked the "travel ready center" on their website and it says "United’s flights from Newark to Rome are COVID-tested flights." and then says that I will have to take a covid test 48 hours before the flight and one upon arrival.
Hopefully, it's a moot point and Italy opens up with just confirmation of having been vaccinated. If not, it is a covid tested flight.