Hi Peter,

This is a quick note to let you know that I am researching on this issue
and will get it back to you ASAP.

I appreciate your patience.

Sincerely,
Linda Liu
Microsoft Online Community Support

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Hi Peter,

We could make use of a Win32 API called SHGetSettings to get the value of
the property indicating whether extensions in the shell is visible or not.

The following is a sample.

using System.Runtime.InteropServices;

public struct SHELLFLAGSTATE
       {
           public Byte res1;
           public Byte res2;
       }

       const int SSF_SHOWEXTENSIONS = 0x02;

       [DllImport("shell32.dll")]
       public static extern void SHGetSettings(ref SHELLFLAGSTATE SFState,
int mask);

       private void GetSettings()
       {
           SHELLFLAGSTATE SFState = new SHELLFLAGSTATE();
           SHGetSettings(ref SFState, SSF_SHOWEXTENSIONS);
           if (SFState.res1 == 2)
               MessageBox.Show("Unchecked");
           else
               MessageBox.Show("Checked");
       }

Hope this helps.
If you have anything unclear, please feel free to let me know.

Sincerely,
Linda Liu
Microsoft Online Community Support