The app is often out of date (it's offline and only updated about once per month) and therefore is not a reliable planning tool. It also doesn't limit in any way the trains you can use (some countries are missing completely but Interrail is still valid). If, by the time you're travelling, the train stil doesn't show up in the app, then you can always add it manually.

If a train shows up on a national website, then it exists and you can book it. MÁV now seem to offer online international booking for Interrail reservations (in any case for this train), so by all means book it there.

Thanks so much for the reply!  I am wondering if I book it on the MAV site it would mean a cost in addition to my pass though, right?

I see on their site other “discount” things you can add, one of which looks like another rail pass but there is no mention of Eurail.

Yes, basically all night trains require an additional cost. This is the case no matter if you book it via the app or the train operator’s website (most of the time booking via the operators will be slightly cheaper). For this train, it seems to start at 33€ for a couchette reservation.

On their site you can add the discount “Bérlet (pl.Interrail)”. I assume this is the Eurail discount as well since “pl.” means “for example”, and from my understanding there are no trains that accept only interrail or only eurail.

Yes, use “Bérlet (pl.Interrail)”. That seems to mean "Season ticket/Pass (e.g. Interrail)” so that's totally appropriate for Eurail.

Thanks so much, everyone!!