Cameras in your fridge and pantry to keep tabs on what you have, computer vision to take inventory, clustering to figure out which goods can be interchanged with which, language modeling applied to a web crawler to identify the best deals, and then some conventional code to aggregate the results into a shopping list
Unless you're assuming that you're gonna be supplied APIs to all the grocery stores which have an incentive to prevent this sort of thing from happening, and also assuming that the end user is willing, able, and reliable enough to scan every barcode of everything they buy
This app basically depends on all the best ai we already have except for image generation