We can link to Aurora Store’s privacy policy which includes all the device data being sent to Google or even discuss some of this ourselves.
This part should also be reworded: “You can optionally log in with your Google account with Aurora Store to download apps you have purchased, which does give access to the list of apps you’ve installed to Google.” This is because the list of apps you have installed is sent to Google when using Aurora Store by default (mentioned in privacy policy), logging in with a Google account just ties the list of apps to your specific account.
To get around sending your installed apps to Google, you can turn on the “Aurora Store apps only” setting under “filters”. you can manually blacklist all your installed applications from the dedicated “Blacklist manager”. We should recommend users do this immediately after installing Aurora and before logging in.
Further Reading:
Edit: Fixed incorrect information