The mistake is that 26mm is the 35mm-equivalent focal length, not the phone lens’s actual focal length.

For angle-of-view calculations, you must use the real focal length of the lens and the matching sensor dimension. For the Galaxy S7, the actual focal length is about 4.2mm, while 26mm just describes how its field of view compares to a full-frame camera.

So your 12° result is far too narrow because it used 26mm with a tiny phone sensor. Recalculate using the actual focal length and the correct sensor size. That will give a much wider angle of view, which matches normal smartphone photos.

Also note:

• You need the exact sensor dimensions, not just the “1/2.6 inch” type label by itself.
• Angle of view can be quoted horizontally, vertically, or diagonally. Make sure the sensor dimension matches the one you want.
• For fitting a standing person, vertical angle of view is often the most relevant if the phone is held upright; horizontal if held sideways; diagonal only if you specifically want diagonal AoV.

So the method is fine — the input focal length was the issue.