When bourgeois revolutions happened and replaced feudalism, in many countries republics also replaced monarchies. But in some places like the UK there are still monarchies in place, even though economically these places are most certainly capitalist and not feudalist.

I have a few questions regarding monarchies today:

How does the royalty function within capitalism, while taking class into account? Previously the bourgeoisie seemed to be at irreconcilable odds with the nobility, while today it doesn’t seem to be the case. Is the royalty even still considered to be a different class? Or are they just bourgeoisie with more bells and whistles?

What role do monarchies still play in politics today? Also how does royalty in different countries differ in their role? Does the royal family in Saudi Arabia play a more significant role than the monarchy in Britain, for example?

Thank you very much for your answers, you are all very helpful!