[bruckie]

Yes, it works completely offline, including transcription and recognition of music. There's an optional cloud sync feature, which I assume is the reason for the notice on Google Play.

(Work for Google, don't speak for them.)

[capableweb]

Thanks. Whose the third party that might get access to the audio? First party would be me, second party would be Google and then the third?

[bruckie]

I think it's just Google for backup, or other apps via Android's standard sharing sheet. You can read the details here: https://support.google.com/pixelphone/answer/9516618?hl=en