The situation in Austria is fundamentally different than in Hungary.
In Hungary the government kept prices of energy and food down by law for quite some time when everywhere else prices where rising. What they see now is the catch-up effect after those restrictions fell.
I actually do not know what is the reason why the Austrian inflation is still that high. Energy prices as are like before covid, but food prices keep climbing. Maybe because the largest retailers Billa and Spar have almost 70% of the total market share they can do what they want (with the clients and the producers)
I guess we also have to wait for one or two years that real estate/rent prices start going down for real (real estate prices are almost stagnating now, but rents are still rising). That may have a real impact on inflation.
The Austrian inflation problem is easily answered: wage inflation (collective bargaining agreements), paired with high gas costs, paired with many inflation linked contracts such as rents. Many of these feed back into the inflation basked and just make inflation quite sticky.
I cannot judge what "EU average" is. I can only tell you that the gas price that a household customer pays today is still twice than it was before this crisis and that is reflected in wholesale prices if you compare the cost of gas in Austria compared to 2020 and earlier.
