With a small float and Saudi state owning the other 98% it means that high price can be maintained with little inflow, but global passive equity investors are mandated (I think?) to hold a big chunk of this overpriced equity due to the huge market cap. Anyone know if that is correct?

According to [1] you can have float-adjusted or market-cap weighted indices.

> An example of a company in which float-adjustment comes into play is Amazon (AMZN). The online retail giant's overall market cap is estimated at around $130 billion. However, only about two thirds of its shares are publicly traded. The non-publicly traded shares, controlled by insiders such as founder and CEO Jeff Bezos, would not be included when determining a company's weight in a float-adjusted index. Incidentally, a company's full market cap, including both its float and non-float shares, is used to determine whether it belongs in the index.

So it depends on the index.

[1] https://www.morningstar.co.uk/uk/news/124023/understanding-p...