I have a housekeeper and I grew up in a house with one too, no I’m not that poster who Harry sneaked into her flat to use the loo. 
I think it really depends on the family’s lifestyle.
ours doesn’t cook meals, but sets the table and does the cleaning after, also she doesn’t do the regular food Shop . She knows I do fresh food on sat/Thurs. but if something runs out, she would go and buy it.
she does the household cleaning agents, kitchen/toilet rolls..etc. order from Ocado or Amazon.
She will do the laundry, mending. general house cleaning, floors need special care and she does an excellent job.
Call/arrange for service for things like boiler/WiFi /washing machine carpet cleaners ...etc
Returns/store pick up.
She doesn’t do babysitting duties regularly , we have someone come in at the weekends, but If we are out for the evening on weekdays she doesn’t mind staying a bit longer, or spends the night.