On my last tour (2019), I took two trains from Vienna to Bolzano, in northern Italy. I had to buy a separate bicycle ticket (reservation) for €3.50. The train was very crowded and the hook for my bike was 3 cars away from my seat. Maneuvering through 3 crowded train cars carrying 2 panniers wasn't easy. I switched trains in Innsbruck. There was a place to hang bikes here, too, but the stem of my Bike Friday was too long for the hook's position. But, the train wasn't all that crowded and I was allowed to shove the bike against the side of the car where I was sitting.
I have since bought a bag designed to hold a folded Bike Friday. I haven't had the opportunity to use it yet, but figured I would carry it so that the next time (should there be one) I take a train in Europe, I can simply carry the bike onto the train without the hassle of a special ticket or the need for a reservation. We'll see how that goes.