Whether inequality worsens or not is a political choice, not something inherent in a technology. Technology creates well-being with decreased toil inputs. How we distribute the production depends on how you vote.
Automation tax is not the solution, we actually want all the sectors to automate instead of giving tax incentives for not automating. So we need increased business, capital gains and wealth taxes across the board to compel businesses to automate.
The taxes can pay for a UBI, and automation makes everything free. After a short transition time people won't need money for anything, and so no amount of money is enough to pay for anything. Money becomes both priceless and worthless.
AI is not for making money, money is for making AI.
AI to hit 40% of jobs and worsen inequality, IMF says - BBC News https://www.bbc.com/news/business-67977967