Direct political power is one thing, but indirect political power is very much another. The monarch gets briefed in advance on pretty much everything. Where there’s direct commercial impact to the crown’s businesses the laws are often changed to favour them.[1] There’s also a wide range of exceptions written into the UK’s legal system after direct political pressure specifically for the royal family.[2] This might be done in the shadows, but done it nevertheless is.

[1] https://www.theguardian.com/uk-news/ng-interactive/2015/may/...

[2] https://www.theguardian.com/uk-news/2022/jul/14/queen-immuni...