Typically you carry your groceries in a bag. Some people have wheeled bags for bigger trips.
In neighborhoods with a traditional urban form (or "15 minute cities"), you wouldn't usually take mass transit to the grocery store, it's within a short walking distance. With groceries close by, it's natural to make frequent, smaller trips.
When I lived in a condo with a shopping center ten minute walk away I still found myself driving it. Sometimes I carried stuff back but it felt like it was more of getting some exercise rather than convenience.
In neighborhoods with a traditional urban form (or "15 minute cities"), you wouldn't usually take mass transit to the grocery store, it's within a short walking distance. With groceries close by, it's natural to make frequent, smaller trips.