What is the explanation of non-zero VCE voltage of an IGBT while its gate is high?
As I'm collecting data upon request of bunker89320, I suspected some other signals. I didn't expect to see any signal between Driver.A1.Emitter and A1.Emitter (the EC point) but when I measured, I saw a weird, half sinus like signal with a 100V peak voltage. When I double checked the application, I realized that the physical locations of IGBT's and my schema are not matched.
Apparently we'd been keeping connecting A2.C to Driver.A1.V_c_sense pin and so on. After fixing this, the signals VGE and VCE observed as expected:

Lessons Learned
Cables weren't numbered and the components weren't labeled in the panel. It was obvious at the first glance that there was a serious documentation problem of the system (any documentation problem is a serious documentation problem). I should have ignored the time pressure of the customer and strictly required completing the documentation before starting any kind of debugging session.