UPDATE: I managed to make it works.
I had to convert my project into c++, then fix the usual bugs (AndroidAdvertising_APL.xml, UnrealEditor-Advertising.lib, build.gradle and GooglePAD_APL.xml).
I then packaged the game a first time, uploaded it on the Play Console, downloaded it, and only after that I was able to launch it from the editor.
And spoiler: they still haven’t fixed the IAP problem 