Gender Roles In Different Cultures Reveal A Lot
An interesting thing about the entirety of human history is that "manage the household" has always meant this: The model that emerged in most societies, with a few unusual exceptions, was the women doing lots of farming and manufacturing work, managing the money, broadly running their house as a small business. Meanwhile the men did jobs that involved higher risk and higher potential reward, which they were able to do because their wives were keeping the household steady. They would often be practicing more artisanal crafts, working down the mines, or going raiding/ warring hoping to bring the family back a military salary or plunder.
If you look at the least industrialised societies today, it's often the same thing, women doing most of the daily work to sustain the family, men trying to improve the family's status with a big win. One of the reasons that many more rural Islamic societies have struggled to industrialise is because the high status activity for men to became studying the Quran. In low industrial Islamic societies, the women work and the men philosophise, because being a virtuous Muslim is more important than bringing in resources.
It's really important when looking at history to not get your view warped by the gender relations of the middle class fantasies that emerged in small but visible slices of the 20th century. These happened because the work that women historically did got automated and outsourced much more than the work that men did. This sort of "strong patriarchy" has always become most prominent in societies with either large amounts of slavery or a lot of trade wealth - the Romans and Greeks, also the Southern US, developed models of femininity that barely involved doing anything, because the work women would do is getting done by slaves or is being brought in on ships, so men don't need to select wives for productivity and can select for status signals instead.
The Viking model is the norm, not the Greek model.