OK, I got your drawing and sure enough I couldn't add points. So I started looking at the settings and see that the next point number is set to 7021, but there is already a point 7021 in the drawing. So I go to Toolspace->Settings->Point->Edit Feature Settings->Next Point Number and change that to 7022, Apply & Close. I can now add points.
I just tried to duplicate this in a new drawing. I set 3 points, 1-3, then attempted to change the Next Point Number setting to 3 and I got a warning message that the "Point number must be unique". I tried to do the same in your drawing and got the same warning.
So, I don't know how you got to that point, where the next # matched an existing number. Nor do I know why C3D didn't see that and automatically increment the Next Point Number value. But it can be worked around if you run into this in the future.