Are two Covid tests needed if plane layover is in another country?

I think the answer may be “It depends”, lol

Right now, none of those countries requires a Covid test from vaxxed travelers from the US nor does Italy require travelers from the US or any of those 3 countries to have a Covid test. That may or may not still be the case in October.

I like the Sherpa travel site for figuring out restrictions between countries.

https://apply.joinsherpa.com/travel-restrictions?affiliateId=sherpa&language=en-US

Right now, no, I do not think any countries require a covid test for transfer passengers, but yeah, in the height of the pandemic, a number of countries did. For diseases, October is a number of lifetimes away. The safest would be to fly direct, but being honest, if things get bad again, that might be the least of your worries. At this point, I just book the best route and do not worry about testing and covid requirements.

Now- No
October- who knows?

Now you will need a COVID test to return to US
October- who knows?

If on one ticket and just connecting, most likely not. If required, one covid test should be sufficient to get you to your end destination (Italy). When testing was the norm, some countries had requirements that a test was done xx hrs before departure (1st leg) and others xx hrs before arrival. The xx hrs before arrival might be the more challenging one when connections were involved.

You can probably look into what Italy testing requirements were earlier, and my guess is that it will be similar if they need to reinstate it.

With the mounting pressure from the travel industry; my sense is there's a good chance the US will drop pre-departure tests for vaccinated travellers soon. But who knows?!