Isn't the electrical system of a BBS02 supposed to be isolated from the bike frame?
If that would be the case, the positive from the battery touching the frame shouldn't create any sparks.
Assume the bike frame is battery gnd, (It could be as it was used as gnd for bike lights when we still had dynamo's powering them.)
than basically, connecting battery positive to gnd is shorting the battery. If the buildin BMS board has a shunt resistor to measure the battery current, this is likely the first and only thing that will burn out.
If the bike frame isn't battery gnd, the situation is worse as you don't know how the battery voltage found a return path to it's battery gnd. It's very well possible that a low voltage wire like a hall sensor one already was in contact with the bike frame and that connecting the battery voltage to it simply burned out that device or the controller input connected to it.
So, after fixing the wire, does your display still turn on?
If it doesn't, you should check if you still have voltage going to your motor.
If I read correctly, the battery voltage is going to the display and when it's turned on, it passes that voltage to another wire so that the motor electronics wake up. Even with a defective motor or controller, you should see something on the display when you turn it on. (At least that's what I would expect.) If it has no communication with the motor controller (defective controller?), I would expect it to display an error message. If the controller still works but something went bad in the motor (like a bad hall sensor), I would expect another error to show up on the display.
It isn't normal to start with that something (not being battery gnd) is making contact with your bike frame, so you should figure out that issue first. (If it's the case)