Yea, it's kinda hard to say how things would have shaken out. I think Sun was reasonably wary about J++. Microsoft's way of operating at the time was "embrace, extend, extinguish."
Microsoft brought out Internet Explore (embrace), added ActiveX (extend), and pretty much extinguished Netscape. All websites could run in IE, but not Netscape - and users are going to use the browser that works for all sites.
Sun's lawsuit against Microsoft wasn't quite about adding native GUI features to Java as much as Microsoft breaking Java compatibility. Microsoft removed JNI (Java Native Interface) and replaced it with J/Direct. Microsoft wanted Java programs to be platform-specific with Java being "just the latest, best way to write Windows applications" (according to documents from the trial).
It's not like Microsoft was trying to create MAUI back in 2000 (the new C#/.NET multi-platform app UI). Microsoft was trying to make it so that Java apps wouldn't be cross-platform by both breaking Java programs that used JNI and making sure that new programs would be made with J/Direct and their Windows-only GUI.
Today, we see a much friendlier Microsoft. It's wonderful. They're happy to coexist with lots of people and ecosystems, lots of Microsoft employees use MacBooks, and Azure is one of the largest operator of Linux servers in the world - and they've made a wonderful business out of this coexistence. Back then, Microsoft would kill everything it could find to keep its dominance. There was no friendly help. There was no "oh, we're just trying to make the GUI better." It was "if we make the UX better via a proprietary native UI, we can get developers using our UI toolkit from Java which means that users are still locked into Windows, it means that the Mac will still be starved for applications, and it means that new operating systems like BeOS won't get a library of applications to bootstrap from if they just add Java support."
It can be hard to remember how much Microsoft tried to break your toys - especially when today they seem like the company that's trying to make cool toys for me and make my current toys better. Proprietary Microsoft Office formats to keep people locked in, telling PC makers that if they offered alternative operating systems as an option they'd lose access to Windows, and taking anything that showed promise and adding something to it to break compatibility with cross-platform implementations (Java, the web, etc)
C# got created because Microsoft got locked out of their embrace, extend, extinguish strategy with Java. Their Java license mandated that they maintain compatibility and they didn't - and to be frank, it seems that they didn't break compatibility with good intentions.