Some places use their own app. I've done that, but for the more typical takeout & delivery food, like pizza, Chinese, etc. Not for what might be considered more of a sit-down dinner. I wonder how you send an undercooked OutBack steak back to their kitchen for more time on the grill?
Over 10 years ago I was using a supermarket's own computer program to order groceries for home delivery, virtually everything they offered in the store. But if they had a mobile app I couldn't have used it, no smartphone at that time, just flip.
The program was very sophisticated. You could browse items by category, like dairy, produce, meats, etc. You could also ask to view items by brand name, or specific type, such as laundry products. You could click for larger views of product packaging, and in many cases link to the manufacturer's web site for more info. That way you could actually have MORE product info right at home than you'd have browsing store shelves in person.
It also could show you only items on reduced store sale, or manufacturer's own promotionals & sales. Your last shopping list could be viewed, which you could simply click to have it repeated, or you could edit it, to delete, modify or add items. There was also a favorites list you could create for yourself. I regularly used those tools.
Delivery was scheduled in 2-hour windows, a chart showing what times were open, over the next several days. If your purchase was over $50, as mine always was, there was no $5 packing charge (you could also have boxes prepared for your own pickup at the store). Home delivery was also $5, which wasn't a big percentage on my typical bills of over $100. The delivery guy was prohibited from taking tips, and he'd carry your stuff right into your kitchen. I thought the process was very convenient and a good deal, since I hate grocery shopping, and I was living alone at the time, already disabled so that carrying heavy bags was tough for me.