I recently came across this app Purchase Apps, which is somehow able to retrieve apps I\'ve paid for in google play after I signed in using my google account.
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you can get the package name of all installed apps on device and then get the information of every installed package that you find in the device from google play without any need to get to user account. there is some third party or unofficial apis to get google play apps details as json by getting the app package name. for example: https://42matters.com/ then use the received information for every package to find free ones.