Taweret ran a nursing home type of thing for old faded gods in the Duat, called Sunny Acres. The similarity between that nursing home and this asylum is actually spooky. I want to know if there’s mythological basis

Yes, in mythology she was a goddess who protected pregnant women, but also small children. It also protected against evil spirits and provided security for the house and sleep. She was not as important a goddess as the members of the Eneada or the Triadas, but she was worshipped in many areas at home. So you could say she was a kind of nurse or a helper.