Pro-tip for folks with multiple adults in the household - Google Keep makes for a super easy way to manage shopping lists.
I created (over time) a list of things we buy, in order of how you'd shop for them and shared it on Keep. Basically me or my wife can pull open the app, check a box.
Get to the store and just go down the list as you walk through the store.
I'm sure others have better ideas - this one works for us!
We do the same thing. Keep is superior to a written list - you can organize it, so apples don't end up near the top of the list, and oranges at the bottom, and you end up walking back and forth through the store.
You can have sub-items in Keep, by dragging items beneath a "heading" item, and so we have a bunch of major items (meat, fruit/veg, breads, paper, cleaning, etc.) that stay on there, and we add subitems to the list. It makes it much easier to shop, and as we shop, we check items off.
It's too bad Google separated Keep from their assistant function. You used to be able to say "ok google, add cheese to the shopping list" and it would go in the Keep shopping list. Now it goes in a shopping list that is somewhere else, that I can't share. Not very useful. Keep is also easily replaced by a variety of open source solutions, whenever Google decides to deprecate it. It is simple, and it works for now.
FWIW, Google Assistant can now use custom list apps (and Keep is an option), so "ok google, add cheese to the shopping list" is a thing again. Under assistant settings, it's in the Services / Notes & Lists heading.
I know you can also do it through Apple Notes. It's a bit clunky to share the note with someone else, but once you've done it, it works very similar to Keep.
I created (over time) a list of things we buy, in order of how you'd shop for them and shared it on Keep. Basically me or my wife can pull open the app, check a box.
Get to the store and just go down the list as you walk through the store.
I'm sure others have better ideas - this one works for us!