Does raising taxes on the wealthy actually cause them to leave?

On one hand, when I think of where wealthy people live, it’s generally New York and California; two areas with very high tax rates

On the other hand, some billionaires have notably left their state. Jeff bezos went to Florida and Elon to Texas, I think? So maybe there is some truth to it?

Then I think of places like Dubai that seemed to specifically target rich people to move there with favorable tax incentives. As far as I can tell, it seems to have attracted many wealthy individuals. However if it was true that rich people just move where they get the best tax incentives, I would have expected far more people to move there