I haven’t tried it myself (tho I’m planning to do so soon), but check Onju voice, it tries to do something kinda similar.
I hope someone tries do pull that on an echo dot. Good hardware, shit software.
Edit: Update with related links.
The Onju Github i forgot before, tho it’s linked in pcbway. It has instructions to set it up along with home assistant and even a matrix bridge.
Onju voice satellite is a different project using the same custom pcb. This one looks better integrated with home assistant and has an actual wakeword system (unlike og onju, which doesn’t have one by design). This one feels more like “better private alexa for home assistant”.
Google is an advertising company first, everything else second. Of course they shouldn’t be trusted, it’s safe to assume they’ll log and analyze the smallest piece of data