FWIW that's not even how Alexa or Google Assistant work. Both listen locally for the wake word with onboard processing, and only when they recognize it do they send the audio stream to the server to fully interpret.
You can test this in a couple ways: they'll respond to their wake word when the internet is down (but have an error response). You can also look at the outbound data and see they're not sending continuous traffic.
Not to say with the proprietary products that they couldn't sneakily change this on the fly and record everything, maybe even turning it on for a specific device or account.
Try to live without it. It's almost impossible. I try to use Librem 5 as a daily driver, with hardware kill switches and GNU/Linux, and it's not always easy.
You can test this in a couple ways: they'll respond to their wake word when the internet is down (but have an error response). You can also look at the outbound data and see they're not sending continuous traffic.
Not to say with the proprietary products that they couldn't sneakily change this on the fly and record everything, maybe even turning it on for a specific device or account.