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Kind of. And there's many over the history of thos operating system as they evolved. Have a look at https://en.wikipedia.org/wiki/List_of_widget_toolkits#OS_dep...

Does it make sense to have a common rendering engine library that is common to both browsers and GUI desktops?

So something like a react rendering engine but the type of nodes change when you use it in different environments:

1. Using it on desktop for GUI: The nodes are like the native GUI elements for that OS

2. Using it on the web: the nodes are whatever HTML DOM nodes that have to be rendered