1. Open your purchased icon pack and choose Open in Stream Deck when available. Allow the browser to open the app.
2. Select a configured button in Stream Deck.
3. Open the icon menu in the property inspector and choose Open Stream Deck icon library. Select an icon from your installed pack.
Extract the ZIP download first. Select a configured button, open its icon menu, choose Set from file, and select the supplied image. You can also drag the image onto the icon preview in the property inspector.
Select each state and assign its icon separately. Changing the icon does not change what the button does.
Screenshot below: the Stream Deck property inspector. Interface appearance may vary by app version.
Official Elgato guide: customizing key icons