But I have never seen anyone talk about these casks holding pressure, so I don't know how much if any carbonation they could withstand. From a standpoint of their construction I know the sidewalls could handle an immense amount of pressure, but the end caps I am not so sure how they are secured.
I don't think the barrel in your link can hold much pressure.
Look at my barrel, made for dispensing carbonated German beers.
The walls and caps use 1-1/4" wood.
Compare the walls to my Wine/ Whiskey barrel, 1/2" wood.
My bier barrel has a coating inside to prevent wood flavors.
German Beer Barrel
Wine or Whiskey barrel
Old traditional way of coating a barrel