How do I check in Android which applications have registered their document providers? I hope no code is needed (I need it from user perspective), but if that's the only way then I can attempt that.
I assume were referring to the file types the different apps can open.
On a rooted device you can get the list the following way:
The mime types and the applications for the default user are stored in the file
Therefore you can execute the following PC to get the full list on a smartphone connected via USB (an enabled ADB):
adb shell "su -c 'cat /data/system/users/0/package-restrictions.xml'"