I have heard that income inequality has decreased in recent times of high inflation, but I do not have a source for that. Who is worse off depends on the inflation. If wage inflation is bigger than price inflation, then that is good for working class, and bad for margins of business and associated stock prices. Hard assets generally climb in price though they may just maintain their value.
In the past 10+ years we have had low wage inflation but high asset inflation. I think this has been helping the rich.