Yes there's a script you can use to do it. Search it on the home assistant forums. Not easy to set up but it works.
this post was submitted on 05 Aug 2023
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Home Assistant is open source home automation that puts local control and privacy first. Powered by a worldwide community of tinkerers and DIY enthusiasts. Perfect to run on a Raspberry Pi or a local server. Available for free at home-assistant.io
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Don't think so, last I checked you could only use commercial voice assistants to add to your shopping list via an app like ifttt. Details here.
Thanks all for the tips on this. I will explore the IFTTT + todoist route that seems to be the only current option to get the Alexa/echo shopping list integrated with HA's