Yes you can, but it's fully booked on 5 August.

There are still seats on the Zürich 21:40 to Vienna 7:58. In Vienna you can take another train to Budapest.

The 3 euro reservation shown there is only for the Eurocity at 3.xx from Salzburg. For the nighttrain you won’t have a reservation in that case. Usually there’s enough space on that part of the train but sometimes still can be busy and if they don’t put the reservation signs there (what happens from time to time), then it can be that you have to move regularly as new people might board...

@MartinM Can I then board the train to Salzburg without a seat reservation?

@rvdborgt The connection via Vienna doesn't make so much sense if I'm not in Vienna until 7:58. With the connection via Salzburg I am already 9:19 in Budapest.

It makes sense in that you can sleep longer. Night trains are not supposed to be fast but more to arrive in the morning at around 8-9 am (ideal time).

No you can't board the Nightjet without a reservation. You could make one on nightjet.com for 12.90€ but do you really want to change trains at 3am ? It'd use 2 pass days btw.

I'd suggest taking the Nightjet (12.90€ for a reclining seat) all the way to Vienna and then take any train to Budapest (second pass day or regular ticket). Yes it'll take longer but you'll have a better night.

I would do it like this?! Then I wouldn't have to make a seat reservation either...
Does that make sense?

@thibcabe 

You still selected the EN (fully booked), not the Nightjet 467 (which has some seats left), arriving 07:58 in Vienna.

You’ll need to take a later train to Budapest anyway.

Select in the filter in the rail planner app “bike carriage” and you’ll see the right train (NJ467) leaving at 21:40, arriving 07:58 in Vienna.

You don't have to make a seat reservation for the EN to Vienna, do you? I can not find the Nightjet 467

You won’t find any free seat, couchette or sleeper on the EN 40467 as it will be fully booked. And it’s actually partly the same train, but one part leaves earlier to Budapest in Salzburg. Whilst another part waits for another train, before continuing to Vienna.

Nighttrains almost always need reservation, and the rail planner is not reliable.

Select in the filter in the rail planner app “bike carriage” and you’ll see the right train (NJ467) leaving at 21:40, arriving 07:58 in Vienna.

On öbb it has unfortunately no more seats
 

I have found the train connection in the app but on the booking page of Interrail you can not find the connection.
What do I do now?

Book via nightjet.com; Start off like you would book a normal ticket, but  add Interrail under your passenger details, as a discount.

thanks i found out :-)

For me there are:

Follow the right steps at www.nightjet.com

Nighttrains in Austria have only optional reservations.

Please note that in Salzburg the Nighttrains to Budapest gets some additional seat carriages to Budapest and they run as EC463. From Salzburg you can be secure to get a seat. Before it is hard to get one because the train like others say is full booked with reservations.

To book reservations with an interrail pass on ÖBB, you select One way ticket option and add as discount card at the data of the passenger Interrail/Eurail Global Pass.

@BrendanDB 

Do I have to buy the ticket on ÖBB with Interrail discount? For 12.9 euros. Do I then activate the trip in the Interrail Pass (use travel day)?

Yes, that's the way to buy a reservation other than Eurail for NJ trains

So if I do not activate the trip in the app, the ticket from ÖBB is not valid? Are there only seats?

In order to travel correctly, you’ll need an active trip/travel day (=that is your ticket), and a seat reservation for the night train (since seat reservations are mandatory).

Normally you have seats, couchettes (a bunk in a compartiment of 4 or 6) or sleepers (max 3 quite comfortable beds per compartiment), with sink or shower on board.

Couchettes and sleepers are sold out, as night trains are very popular and sell out weeks in advance. You’re kinda lucky to still have found a seat.