Tall cabinet with unsuitable top panel

No, the hardware store is definitely not a good idea. Ours here couldn't even cut our real wood countertop because the router wasn't powerful enough for that. In this respect, I also don't consider them competent to cut the boards.

Has anyone ever repaired the chipped veneer of Gnosjö, and if so, with what?

As Nayla already wrote above: Gnosjö is not veneer, but printed foil. I hardly believe that anything can be repaired afterwards if the foil tears. Therefore: sharp saw blade . Greetings and good luck, IKEA friend