I don't have exact numbers for you, but it depends on how you measure it. You could say 0% - there is the browser engine which is largely C/C++/Assembly, and that would likely dwarf everything with all the dependencies on the system. You could say ~100% - the entire shell is Swift with some C/C++ dependencies. You can portray the numbers in whatever way you like to make a point. Instead, I prefer to identify that the browser shell is entirely Swift, and the browser's functionality would not have been possible to build up at this pace without Swift, including the code and engineering sharing that it enables.
The majority of the business logic is shared code. We are using TCA, and that provides for a natural split between the business logic and UI logic. There were pieces which had to be rewritten as there were certain dependencies (e.g. SDWebImage), but they had to be rewritten as they are not purely portable Swift code.
There is some platform specific code that is not shared because there will always be platform differences and we want to integrate with those (e.g. the Windows notification center).
The Swift Windows UI "stuff" is mostly the WinUI bindings which are a separate project which we did open source. We built the shell on top of that, but that is akin to measuring AppKit or UIKit.