I have many completely clear photos of Mount Fuji from when I was there in late March last year. However, I do not have any of when I stayed in the same hotel where you are. Fog completely blanketed everywhere! We sailed across the lake in fog. The next morning I could just see those stone "picnic settings" and the edge of the lake, but no further. Mount Fuji was just a figment of the imagination.
So glad you had such a lovely, clear day there.