Honestly I would be perfectly happy with the service like this, even if I had to manually input what groceries I need. It's still an incredibly complex problem though. AI is probably better suited for it than anything else since you can have iterative conversations with latest generation AIs. That is, if I tell it I need cereal, it looks at my purchase history and guesses what type of cereal I want this week, and adds it to my list, I can then tell it no, actually I want shredded mini wheats.

So it would probably have to be a combination of a very large database and information gathering system with a predictive engine and a large language model as the user interface.