A workaroundWhat worked for me on Android Version 12 was to increase touch and hold delayset the default digital assistant app from Google to None.
This is under Settings >> AccessibilityApps >> interaction and dexterityChoose default apps >> touch and hold delay on Android version 12.Digital Assistant App >> Device Assistant app >> Default digital assistant app
The promptSet to turn on Google assistant wasNone and the prompts should stop coming up after long pressing the home key.
Increasing the hold delay will however affect your experience with dragging apps on your phone, but since this is not an every day action, I think it's a good compromise.