I have had a very unusual experience that has happened at least 3 times over the last year. I command OFF then PLAY WHITE NOISE. The speaker comes back and said "NO NEVER" then BELCHED... We were so shocked and couldn't stop laughing.
That's an interesting event! Belched is also like a burp, right? And your Nest speaker did that. Let's check it out ― a few questions: Do you have a Google Home Mini or a Nest Mini? Since it happened 3 times over the last year, when did it last happen? When you gave the command Off, was it playing music or any of the relaxing sounds? It would help a lot if you could do a sequential reboot first. Unplug the power cord of your router followed by your Nest speakers. Plug them back in after 3 minutes tops. Restarting your phone might also help.
Keep us posted if it happens again.