Yes, this is possible using the Shortcuts app (bundled by default on iOS 13+). In fact I made this exact shortcut earlier 
I plan to add this and numerous other pre-made Shortcut examples to the docs in a few weeks after iOS 14 leaves beta. But for now, here’s the steps to recreate it.
You could either tap this Shortcut on your Apple Watch (I think it only exists on iOS 14) or call it using Siri. If you name the Shortcut “Add to shopping list” for example, you’d raise your wrist and say “Hey Siri, add to shopping list.”
Then it’ll ask you to dictate text, just say the item name like “Pizza.” It’ll add to your HA shopping list and Siri will respond with a confirmation (“Added Pizza to your list.”)