So after over a months, I finally figured it out.
Despite paying a professional electrician to install it it wasn’t done correctly. What was wrong is now obvious to me but not knowing anything about household electricity and assuming the installation was done correctly, I didn’t question the basics.
The key issue is that only one main was being sensed. It was simply because only one of the clamps was attached to a main (see photos). The other one was simply connected to the “Range”, see photos included. Once I figured that out, it was just a matter of figuring out a way to move things around a bit without getting electrocuted and clamping to an actual second main.
Now the monitor is reporting two mains (through one is quite a bit lower the other currently but that could just be a function of us being in the kitchen with no other room lit up).
Now I need to figure out if, as @Maarja-Liis might have alluded to, I can rely on the sensor as is, if it needs to be reset or replaced. It had never detected any appliance after a month. It had detected 250W of always on but I don’t know how reliable this was in this circumstances.
I do feel that Sense support who I relentlessly engaged during that time could have diagnosed the issue better. Instead I was left to my own device (pun intended).