We have an American Standard toilet (I'm not sure of the exact model, but it looks something like that Champion 4). When first installed, it worked great and it was indeed a one flush device. Beautiful it helped greatly.
Now the water goes through, but there is nearly zero pressure so the rest doesn't go through without a plunger...
I'm thinking that this type of toilet has additional pipes that allow the flush to function. i.e. the water doesn't just pour in the bowl, I think it is poured through another pipe and that pipe may have some residue in it prevent the normal flush functionality.
I've been looking for information about that toilet mechanism and I'm probably really bad at searching for it... Do you have any details on how to properly clean such a toilet pipes? Do you have an schematic that would show us how the pipes are actually laid out?
Here is a picture from the side:
In the picture, I added a red line which represents the top of the waterline in the bowl.
As we can see on this picture, there could be a pipe between the water taken and the flushing pipe coming from the bowl (just over the red line toward the left side of the picture).
Also there seem to be a small pipe between the larger pipe just under the bowl and the one going to the ground.
All of that makes me think that there could be debris clogging those pipes.
Just in case, I had a plumber come by and he was not able to fix it. He checked the pipes and they're clean, the water flows as expected, no clogging down there. So that's the toilet which has a problem. It was also snaked, but that's probably old technology on a modern toilet which doesn't help...
As per the answer below, I got muriatic acid and ran the process once to see if it would clean the toilet. In my case, just once was enough to get the toilet to flush like normal again! I needed a funnel, though, because the flushing mechanism is such that I just couldn't reach the hole without pouring the acid all over the place. So I bought a 3 set and I duck-taped the wide one (red) to the long one (blue) for the perfect funnel.