The work energy theorem is indeed a tricky beast and it is easy to misuse it. Unfortunately, most derivations are rather lax about identifying the assumptions in the derivation. Most derivations assume that the system being analyzed is a point particle with no internal degrees of freedom. Your system here has internal degrees of freedom and an internal potential energy. So it doesn’t apply.
When used on systems with internal degrees of freedom it is important to understand that the “net work” of the work energy theorem is not the same as the sum of the work done by all forces acting on the system, which is the total thermodynamic work.
In this case there is no external force, so the “net work” is zero. But because the system has internal degrees of freedom the work energy theorem does not apply and we cannot infer that the KE is unchanged.
What we can do is examine the total thermodynamic work. Since there are no external forces the total thermodynamic work is also zero. That means that there is no overall change in energy and any increase in KE must be associated with a corresponding decrease in internal PE. This is exactly what is observed.
So, the bottom line is that the work energy theorem is very limited in its application. For systems with internal degrees of freedom the concept of total thermodynamic work is more useful.