As far as I know this train isn't available online. ÖBB only works for the later night train as it comes from Vienna. Interrail website will send you paper reservations, fees are expensive.

Either you get a regular ticket online and save the pass day (if the price difference isn't large) or you book at a ticket counter in Romania, probably also possible in other countries.

Indeed, book at a ticket office. Should be possible in e.g. Germany, Austria, Czechia, ...

Thank you for your reply;
I also emailed CFR and they stated the same: you can only book at their ticket counters; The thing is: eurail.eu allow me to book a double sleeper on that train and it comes as a paper ticket like you described. I am fine with that; the thing is that it doesn’t allow me to add travelers. So if the ticket can only be bought on the counters, how is that possible to book individually you see? My concern about buying it at a counter is arriving there and no cabins are available you see?

Yes, that is one possibility. We are going from Prague to Istanbul in some routes of the old Orient Express. So yes, i can try to book it in Czechia, but that is strange how it allows me to do so in other countries and not on the website; in fact, i can book individually a double sleeper cabin, but not add any travelers. And on CFR they allow me to buy the full ticket with the reservation today for that specific date, but it doesn’t allow me to insert the global pass as the main ticket. So, very confusing parts in this whole process :D