Charisma? That is a big misreading
It’s more that he's good at understanding and catering to the desires of a large network of powerful people, whose desires are in conflict with each other.
e.g. Elon was scared of Google / Larry Page and Demis (who he formerly funded), and Elon had money to spend. Sam helped him recruit key minds away from Google
Satya wants to make Google jump, and Sam figured out how to let him do that, in exchange for billions in computing resources
Early innovative researchers wanted a mission that's more interesting than incrementally improving Google, influence that’s more than they had at Google (where there was already senior technical and research leadership), and massive computing resources. Sam figured out how to fund that, by selling the vision to people with money (Vinod Khosla, etc.)
And later employees want to be in a compensation ladder that matches Google, and by all accounts Sam set that up. Ilya and the board probably weren’t worried about the stock option package that later employees got, so that’s a big reason Sam won the boardroom conflict, and why he got to create a friendly board.
It’s basically just trying to get everyone what they want, not charisma. Steve Jobs had charisma because he would personally get on stage and tell a story about products, and many of those stories came to fruition.
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To the degree it's true that Sam didn't take any equity, and agreed to be bound by the non-profit board which could fire him, then I'd say he "innovated" in politics. He let everyone trust him, until they no longer had the power to defy him.
He's basically good at staying at the center of a lot of powerful forces. But if powerful people had different desires, then he would just go with that. I don't see any evidence that he's a visionary or has real charisma.