Telling Google assistant to add items to your shopping list and them being added to a keep note titled "shopping list" was the original functionality in Google keep. I used this feature all the time which is great for someone like me who has ADD. Then without warning, Google decided to change the functionality so that it added the items to Google Express instead. It was a small change that caused a lot of inconvenience and headaches for me. There was a time I would have really cared about this change but considering the inconsistency of Google's products, I really can't get invested in them anymore. I try to degoogle my life as much as possible these days.

I think the issue is that Keep isn't the default. If you use Assistant and create a shopping list, I assume that right now it will default to Tasks, and we all know that there's significant inertia that comes with default settings.

To change it to Keep, firstly you need to know that it's even an option to change it, then you need to figure out how because it's non-obvious.

Talking to Assistant (via Nest for me) to add items to your shopping list in Keep works amazingly well. If you geotag lists, you can have your shopping list pop up automatically when you get to the store. It's the future! (and it's been here for years if you knew how). It's crazy how few people know to do this.