Actually the Seiyu chain was owned by Walmart for some time. They sold most of their share to KKR and Rakuten during the pandemic, but (I believe) still have a minority stake. I was amused to find lots of Walmart store-brand products last time I shopped there several years ago.

There are many supermarket chains in Japan and your options really depend on the neighborhood you're in. For example the best option for price/quality/selection in my neighborhood is Olympic, but where I lived before, it was Santoku or Ito-Yokado. And where I live on the south side of Tokyo, there is a Tokyu supermarket at just about every station, so they are probably the most ubiquitous around the broader area.

Most supermarkets sell a variety of prepared food, like ready-to-eat bento, sushi, katsu, croquettes, karaage, etc., and the quality tends to be better than convenience stores. The Olympic in my neighborhood sells massive (around 1,000 calorie) bentos at weekday lunchtime for about 500 yen. Supermarkets also tend to have very good deals on prepared items in the evening, as they put things on sale to avoid throwing them out at the end of the day.