Not being an expert on this and recently myself also having done a few such, I did also note it was quite a different thing as what most other railways offer. I think it should be possible but only for DOMestic OeBB rides and not for, I assume, your collection of RES for TrenItalia.

This system seesm mostly devised for old-style normal tickets and as these are anonymous, there has to be some way to garantee only 1 is used and for the right way (for only a RES this is much less an issue, but a major reason why railways do not offer this anymore is that many shrewd pax only bought the RES and ´forgot´ to also pay for a ticket for the fare). Hence this rather cumbersome ´print it´-though if you hold many, you could rearrange perhaps your trip to pass at some OeBB/AT stop and get it out of the machine (yes, that works very fast, also own exper.)

Several others, incl angelo , frequent poster from IT, have confirmed that showing the RES on fone (opened and able to show QR code on it) is enough for checks and entry gates

Via ÖBB you have to choose how to get the reservation. If you have choosen PDF, you can't change it more and you show it as PDF on the phone. Or you open the app with your ÖBB account that you used to buy the reservation, you should find the reservation under my tickets.

IMHO,

I always take a printed copy of all e tickets, be they air, rail or hotels.

I still feel it is better to use to demonstrate content than hand over my phone or, worse still , hold it in somebody face.

Just today we were on the Frankfurt to Brussels ICE train. Arrived at Cologne already full. On came the hoards  many with reservations. Obviously many were occupied by non reservation passengers, others in the right number but wrong coach.

Many papers were flapped but few phones.

Most were settled but a few were very difficult.