Great post, with one caveat

the closest thing to a definition we have for “vegetable” botanically is “literally all plant life and maybe also some fungi,”

I got my degree in Ecology and Evolution, and we always used a similar working definition but it was “edible parts of a plant which are not fruit.” So basically botanically, stems, roots, leaves, flowers, and all subvarieties of those are vegetables. Fruits are fruits. Fungi are fungi.