humdrum23 Android/data/, Android/media/, and Android/obb
Yes, accessing those folders require root access.
humdrum23 I'm wondering if there is a way to back up app data (settings, save games, etc.) for apps that are missing an option to export these things. A full phone backup is not feasible for me here I think, since it is for moving some apps to another user profile rather than another phone.
Yes, this can be done by using the system backup feature in the Settings app > System > Backup. It allows you to select only individual apps to back up, so you don't need to back up every app or system setting. When you start a new backup, you can select which apps to back up. After you have set up the backup, you can select "Backup status" > the vertical ellipsis top-right > "Exclude apps" to select additional apps you want to back up.
Not all apps will be able to be backed up. I recommend creating a backup and then test restoring that backup in a new profile before deleting the original app.