Will Bitcoin adapt to such computational power, or could supercomputers make existing blockchain security obsolete?
There were modern computers before the existence of bitcoin and those couldn't crack through the blockchain tech, in same vein am believing that bitcoin developers are also working in enhancement of the blockchain against such advance tech in the future like the quantum computers.
What about mining, will supercomputers centralize it and put power into the hands of a few?
Perhaps that's exactly what we would be seeing years from now when quantum computers become mainstream. Take Tesla cars for instance, not everyone could afford it even after since it was created, and that's how it's likely going to be with quantum computers and those few who could afford it would majorly have a central monopoly of the bitcoin mining.