I read your description going through the thread and noted how similar our personalities are. In my family H does many of the things your W does, even some cooking (not a lot though). He fixes everything and was the one who helped our kids with any “hands on” school project. He even went along with them on field trips.
I handle “our” email conversations and more.
We like dividing things into what each of us does best rather than sharing and one of us being disappointed with what the other doesn’t do as well.
I am the only woman in my birth family and my immediate family right now and I notice I get slotted into some very gendered roles. For my birth family, I am the glue who holds everyone together and is charged with maintaining communication and holiday planning. My mother did this before she died. She was the matriarch, now it is me. In my family, no DILs yet, I fulfill the same role. With my kids I do more listening. They seek me out as a sounding board or as the person to tell big news, bad or good.