I assume the issue is about privacy in your case. I am not using Alexa, Siri, etc.
using a cloud service is much easier and cheaper, but I was not comfortable with that trade-off.
HomeAssistant seems to natively support wake words, but I haven't looked into it yet. I simply use my smartwatch (Wear OS supports replacing Google Assistant with HomeAssistant's Assist functionality) to interact with the LLM
The cam is positioned higher than most things in the room to reduce triggering it unnecessarily.
When it triggers (currently using just simple cvv facial landmark detection) it emits a beep and then listens for a verbal command.