It may be in the controller who knows. All I can say is that the melting of those two pins isn't normal or right.
Are you 100% sure polarity is correct on both sides of the battery contact.
Unless the battery was incorrectly wired up from the factory. I'm the first to open this battery and all I've done is replace the bms swapping cables like for like. Plus I replaced the blown fuse.
If it was the wrong way round wouldn't it work if I connected the battery the other way round? Obviously that's not possible physically but if I connect it using wires. I tried this out of interest and it sparks on either combination.
Out of interest I tested it by first disconnecting everything else from the controller (brakes, motor, hall sensor, display) but it made no difference.
Unfortunately I don't have anything else I can test the battery on (aside from my multimeter?). I think I just have to assume it's the controller.
I'd take it to someone if I knew of anyone local to me (Nottingham) who could diagnose the problem. Googling just gives me a bunch of bicycle mechanics (I was a bike mechanic for 5+ years). I should probably try an electrician but I imagine most want to touch an ebike.