Nah... The "disc" isn't 100% zirconium. I don't know what it's made out of but the zirconium part is just the nanowires which would likely be some teeny tiny percentage of the overall weight. If it's like silicon ICs (e.g. the CPU inside your computer) zirconium would probably account for less than 1% (probably 0.1 or even 0.001%) of the overall weight.

99% of it likely to be "packaging" which is tiny copper wires carefully connected to the zirconium (probably via an intermediary material) to transmit and combine the power along with loads of insulating materials and lots and lots of high temperature plastic (so it can survive short bursts of soldering).

It's a prototype and may not like getting very hot so maybe they didn't use normal soldering methods and might have used conductive adhesives or similar crimping or vacuum welding or other fancy ways of connecting things that labs have access to for such things.