Is it a bug in the design of a low side UCC27524A, and 2EDN7424 gate driver if it doesn't use VDD capacitor?
It seems you know the answer already. If the scope picture is the vdd drooping when the output turns on, then that is evidence that your vdd supply does need bypassing. It is the exact reason for the bypass caps. You might also want to look for potential ground bounce as well. As for any magic solution, sorry. You’ll just have to add the capacitor and spin a new board.