To me that story reads like thinly veiled political commentary. Peasants and feudal lords/nobility/local government working towards a common goal (e.g. paying taxes to fund defense against bandits, building grain stores for times of famine, etc). A person in power misappropriates the funds for personal gain, and any peasant who complains loses their head.
Telling a story about a mouse and a cat allowed you to keep your head, and the situation was probably common enough for the fable to become widely known before it was picked up by the Bothers Grimm.
It's not that different from Gulliver's Travels complaining about pointless religious wars under the guise of talking about far-away islands of tiny humans, or Star Trek criticizing the Vietnam War under the guise of talking about a primitive planet light-years away centuries in the future.
My thoughts were this might also be on the World politics level. E.g. a case where a stronger country during wartime will co operate with weaker country, and then slowly infiltrate because it's easier than to do full on invasion.
Then finally when weaker country starts to complain they will completely take over. The stronger country in theory could at any time swallow the weaker, it's just that it might be more beneficial for stronger country to do it in a slower, methodical, deceiving manner, until it can. Or when it actually needs to.
In this case it seems to me it was strategic behavior by the cat to not immediately eat the mouse, but instead consume the fat first. Eating the mouse was a fallback in this scenario.
But overall this specific scenario happens on so many levels of relationships including, but not limited to interpersonal, business, country level, World level, etc.
The main key points in my view are that it is a cat, and cat always will want to eat the mouse in what you would think is pscyhopathic mannerism if it was between people, but it's most easily explainable on level of countries. Because ultimately countries as entities have to act in psychopathic ways with each other, because territories, resources are all clearly limited.
Due to the complexity of World politics you have to co operate with your enemies as well. Both sides are lying to each other, keeping secrets, but at the same time co operating, because they have to or they otherwise will fall behind other countries.
I hate to break it to you but this is ahistorical, as this story is several hundred years old the peasants at that time had no concerns for world politics nor were they concerned by whom they were governed, the circumstances for them wouldn't change
Telling a story about a mouse and a cat allowed you to keep your head, and the situation was probably common enough for the fable to become widely known before it was picked up by the Bothers Grimm.
It's not that different from Gulliver's Travels complaining about pointless religious wars under the guise of talking about far-away islands of tiny humans, or Star Trek criticizing the Vietnam War under the guise of talking about a primitive planet light-years away centuries in the future.