QP problem infeasible

This

illustrates that the change can be quite deep. I do not say this case is relevant to the example of thread.
What I am saying is that the formulation can have bigger nontrivial consequences.

In my SOCP formulation, is there strict complementarity in exact arithmetic, but not numerically, given solver tolerance? Or is that no what is going on at all n this case?

You have misunderstood my last post.

I am not saying anything specific about your formulation versus my formulation in this specific case. Particularly I am not saying anything about strict complementarity of the different formulations.

However, what I am saying is that strict complementarity can be affected when you reformulate the model. And hence the reformulation in such cases is nontrivial and something deeper is going on. Also I am trying to illustrate there are many things to consider when evaluating the different formulations.