Simply enter the shopping list in the smartphone app and transfer it immediately to the Wear OS smartwatch. No detours via servers on the Internet. The transfer is lightning fast and does not require any additional actions in the smartphone app.
The shopping list can be integrated into the existing watch face as a complication and can therefore be accessed more quickly.
I use this app to conveniently create my shopping list on my smartphone. The shopping list can be easily accessed on the Wear OS smartwatch while shopping. I have linked the app on the smartwatch to a button on the watch, which saves additional time.
The app must of course be installed on both devices ;-)