I can't think of anyone powerful enough who isn't also rich. Although "rich" is a vaguely defined term. There still to me seems to be a direct relationship between money and power - billionaires can push the world further than millionaires, than the upper class, etc.
Money and power are two sides of the same coin. Money is literally the unit of measure for power over other people - to the first approximation, a dollar in hand means you can make appropriate people do a dollar's worth of arbitrary work for you.
The more money you have, the more you have of this kind of power mediated by economy. You can, in particular, use this power to have politicians do work for you (many ways of doing this are perfectly legal). Conversely, political power - the kind mediated by legal systems or explicit threats of violence - is directly convertible to money.
(There's also a special variant of the latter - power wielded by organized religions. The power to browbeat others into doing almost any arbitrary work. Of course, that one too is trivially convertible to both money and political power, and vice versa. That's why fully separating business, church and state is fundamentally impossible. They're different facets of the same thing. An Unholy Trinity.)
A managing partner of a $1B fund is more powerful than a person worth $10B on paper whose wealth is all tied up in a minority position in a company they are unable to sell the shares of.
Or consider the power of Biden vs his personal net worth.
