I do think there is skill at being good at caring for children. Under your taxonomy it would fit best under “management skills”. However I generally expect management types are worse than average at caring for children.
The cliche is of the high-powered executive being an absentee parent. They tend to lack the patience, warmth, emotional skills, etc. to even connect with their own children.
I think you’re definitely missing some kind of relational /emotional skillset here. Nannies, therapists, priests, elementary teachers, hospice care providers, etc.
I’d like to note that that particular problem is that your housemate got a bidet that didn’t fit the toilet. This is a somewhat common problem since the top tier bidet (which certain types tend to want) doesn’t come in the most standard toilet size.
My boyfriend has done the same thing and I find it low grade bothersome. At some point in time, I’ll make him upgrade the toilet to match the bidet. (Because God forbid we downgrade the ultra fancy bidet)