I had the same problem with google home. I already had a shared (with the SO) google keep note for my shopping list. I wrote a google keep integration with an IFTTT app to solve this, letting me do a "OK Google, we need X" to add X to the list.
https://github.com/Resinderate/shopping-list/blob/master/sho...
When I first got a Google home, the keep integration was built in. And then they moved it to Google Express shopping list, suddenly, which was infuriating. Ended up using ifttt with Asana. Will try with keep as I preferred keep for shared shopping and Todo lists.