The radius of the Earth orbit increases by about 15 cm per year. One of the main argument found online to explain this is the fact that the gravitational pull of the Sun on the Earth diminishes over time as the Sun looses mass trough nuclear fusion.

Now I would assume that the total energy of the Earth-Sun system remains unchanged as the change in the mass of the Sun is an intrinsic process.

The total energy of the system, using the virial theorem and assuming a circular orbit, is:

$$E=K+V=\frac{V}{2}=-\frac{GMm}{2r}.$$

But to have a constant energy over a diminishing mass requires that r diminishes, so I don’t understand how this argument is used to justify an increasing radius.