Aka the speed is negative 10
As I have said, I'm not a pilot, I'm a winemaker with an interest in aviation. I think we are confusing aviation terms with physics terms. I am thinking in physics terms; speed is a quantity, a magnitude, and combined with the direction of travel generates a vector. The length of the vector is the speed, the way the vector points is the direction. The vector sum of the wind speed and the slowly retreating Cessna is the resultant that defines the aircraft vector. In this case the speed is 10 knots and the direction is along the negative X axis. The speed is not negative, the resultant of the vectors is -10X after one hour. The plane has traveled 10 nautical miles in a direction opposite to where the pilot wanted to go.
When you are discussing ground speed I assume you are thinking in aviation terms, but this whole thread is not about aviation terms, it's about somehow magically gaining energy when turning windward in a steady wind environment. This seems to me to indicate that we need to treat this as a physics problem, not an interpretation of 'ground speed' in the aviation sense.
So call the Cessna's ground speed -10 knots/hr if you wish, and I'll call it 10 knots/hr at angle Θ, but I think we mean the same thing.