poubellier Nothing will happen if you try to install the app from Obtanium when you've got the app installed from F-Droid in another profile. It just won't work. Due to the different signing keys as you say.
You need uninstall the app from both the user profiles first. You might want to backup the app data before uninstalling if necessary.
If you later want the app installed in both profiles, you can clone the app to the second user profile using the functionality provided by GrapheneOS. In addition, when you update the app in one profile, it'll be updated across all profiles.