As you will buy it via Interrail/Eurail, supplement is included as stated on the website.

But always best to book this via the operator (here ÖBB = https://shop.oebbtickets.at/en/ticket?cref=oebb-allgemein).

So no extra payment is needed, when booking it like an ordinary ticket with interrail/eurail selected as discount under passenger details.

Find the exact steps to do this on ÖBB here too:

My only concern is that if I purchase the seat reservation and during the journey, the inspector still requires me to pay the €10 supplement fee plus the extra €5 fee onboard the train. Then it would not make sense to purchase the optional seat reservation.

Just follow the steps mentioned in the link in my second post “how to get reservations”, and you’ll be good.

Best to reserve this stretch anyway, very popular route.

As long as you buy it on ÖBB it'll cost you 10€ for the surcharge (Aufpreis) + 3€ for the seat reservation (very much recommended).

Add Eurail as a discount and select one-way tickets as advised. 

Also use tickets.oebb.at for Italian journeys, there's no booking fee compared to Eurail !

The reservations on ÖBB does not include seat reservation, just the supplement fee? Will there be a situation where you paid for the supplement fee but not the seat reservation and the train is full, what might happen?

Than you’ll need to stand, sit in the bar car or find an onoccupied seat. (Seat reservations are lifted after 15 min of departure, so if someone doesn’t show up, you can sit there).

The stretch from where to where the seat is reserved is indicated on small screens above the seats.

Okay, thank you.