we learn that women can not stay idle at home and are supposed to be busy at something, right?
Eshe Chayil lists lots of things to do in a normal household. By now, men, with Hashem’s help, automated most of these activities. Women world over, follow the halakha above, increased their standards of cleanliness and tideness to the level that never existed in history, but still … So, if women are to only stay home and, in many Jewish families, send kids to schools and often using household help (sometimes cheap even if not very legal) – they should be doing something useful. They could teach their kids at professional level, for example. If not, then there is a question about even volunteer stay at home. [My wife did while kids were little and she was fully engaged with them].
As to women who want to work outside, I agree with Gadol here, there are plenty of precedents of women working and having businesses. It is possible that some Rabbis give public advice as a desirable social policy, but that does not mean that specific individuals can not balance home and work.
Also, notice that “not leaving home often” in old times does not mean that the woman will be doing only housework. People were running businesses from their homes all the time. She could be weaving baskets, running a school, a restaurant, while infrequently going out. Being a traveling salesman (and still is) not a good job choice. Now, with WFH, we came full circle and frumme women can do heart surgery online without leaving the kids.