Would a real cat actually ever eat porridge of any kind?

In English we have the saying "To beat around the bush" which I think has a very close meaning. More or less, to circle around the topic without addressing it directly. I believe it comes from the idea that people would use sticks to hit a bush in order to chase out any birds hiding there (for hunting). Either way, I don't think this saying has much to do with actually feeding porridge to cats. I think it is more related to the way that a cat moves when it is uncertain, hesitant but quick and graceful, and the qualities of the porridge- something that is appetizing but can hurt you quite a bit because not only is it very hot, but sticky, so it may cause a bad burn.

For the more 'actual cat related' aspect of the question, most cats don't seem to like to eat porridge, but some are indeed interested in typical human foods and will try to sneak a taste of anything. I know someone who has that cat that has stolen and consumed entire loaves of bread, drank from a cup of coffee when it was left unattended, and other things that most cats wouldn't touch. Many cats find butter very enticing, so porridge with butter might be tempting to any cat.

I can't find any information that suggests that people used to intentionally feed porridge to cats on a regular basis. In the time before processed cat food, it was common for people to put the cat outside at night to hunt, and so feed itself. This was usually supplemented with table scraps, inexpensive meats or meat trimmings and bits/organs that people wouldn't eat, and sometimes broth, vegetables, milk or bread.

Cats are obligate carnivores, so they need meat (or potentially a complex set of supplements to replace it) to remain healthy. They have some limited ability to digest and gain nutrients from grains, so porridge would be something a cat could eat to avoid starving, but it would not be healthy or survive long-term on such a diet.

I'll try to tackle the German version of the saying: "Wie die Katze um den heißen Brei schleichen" = sneak arount the hot porridge/mash like a cat. Meaning is also circling around the point of interest without reaching (or: being able to reach) it.

The hot porridge term here is far more generic than the contemporary breakfast type of oatmeal porridge. It includes all kinds of semi-liquid based foods. The "solid" basis can be whole grains, groats, rolled/crushed grains, semolina or even flour. (In German, also mashed potatoes = Kartoffelbrei or mashed carrots = Möhrenbrei would be included.) For a Brei/porridge, the starchy stuff is soaked and typically boiled. The liquid can be water (or broth) based or milk based. These porridges or mashes belong to a continuum porridge/mash - potage - stew - soup.

I don't see any cat beeing interested in a water, salt and rolled oats porridge. But those old-fashioned porridges/mashes include lots of savory varieties based on meat or bone broth (think e.g. kasza or risotto), and some of them could also be served with molten butter. Those warm = strong smells would be extremely interesting for a cat, in particular for one that has to hunt for a living.

(Anecdotally, my mother tells of a farm cat that tried to steal chicken meat from a pot where the chicken was boiling for a soup. I grew up with the art of cat feeding being "sufficient so that it will put its territory here, but not too much so it doesn't stop hunting mice".)

I have a sneaking suspicion that the Swedish gröts shares roots with German Grütze (or English groats). Grütze means either crushed pieces of grains that are larger than the pieces called Grieß (semolina) or Schrot (grist). Or it means the particular thick variety of Brei/porridge that used to be made by cooking these crushed grains. Like Brei, Grütze can be sweet (e.g. rote Grütze, with fruit juice - nowadays finer starch ranging from semolina over flour to starch powder is used) or savory (compare bulgur [though Grütze is not usually parboiled]), with buckwheat it is also used for a preparation with the whole grains (Buchweizengrütze). Gerstengrütze (barley groats) is probably still quite close to the original meaning.