Frecciarossa in Italy is included.
Please don't use the rail planner app or the Eurail website to plan. They don't get enough updates to be reliable. Use the local or national planners; for international travel, the Deutsche Bahn website or DB Navigator app is a good choice. For Italy, www.trenitalia.com is most reliable to plan. If the timetable for your travel date is not available yet there, then you're too early. Reservations in Italy are often possible from 2-3 months in advance.
Reservations for Italian day trains are best booked via tickets.oebb.at. Do NOT use the "seat reservation only” option but add the Interrail/Eurail discount and then look for normal tickets. A reservation in Frecciarossa is €10.
Thank you so much for your guidance