Is HS2 still being built in the rural Midlands and South, so that Northerners can get to London quicker?

Yes, it is; but only to Birmingham, in the Midlands. Not to the North as the section beyond that area was cancelled - but HS2 still owns the land it blighted.

I think it will only extend London's commuter area to the West Midlands, it will not serve the towns it brushes past, and I doubt it will live up to the promises or bring any real benefit to anyone.