Should we A) colonise other planets or B) build habitats in the middle of space, like O'Neill Cylinders and stuff?

No matter what you do the Earth won't stay habitable forever. So we either learn to expand out into space as a species or face extinction eventually. Not to mention putting all our eggs in one basket is a terrible idea. Any cosmological event could wipe out the Earth at any time. The question is are you okay with our entire species going with it?

There needs to be a backup, ideally multiple.

I'm not convinced that suspending space programs would create solutions to climate change.