Reservation is optional, but there's a mandatory supplement for this train in Italy, as the rail planner app also says: €10 in 2nd, €15 in 1st class. If the ticket inspector said something different, then they're mixing up things, but you paid the correct amount.

This supplement is always confusing as it is often incorporated into a reservation at the same time.

The first time I did it I booked what I thought was an optional but advised reservation with OBB. It wasn’t until I saw arguments on the train and heard about the supplement on the community I even knew I had bought a combined booking. There was no apparent reference to the supplement but the inspector was happy with my printout from the pdf (which had our seats detailed on it). (Bologna to Munich ECB).