I doubt that .NET has much to do with it. There are just many more JavaScript developers who know how to make UIs.
While they do their best to open source .NET and related SDK tooling, the whole IDE story has been a bit of a mess, rewriting VS4Mac only to kill it shortly after the rewrite reached 1.0, C# DevKit under the same license as VS, the stuff that will never leave Windows or VS to Mac/Linux, Xamarin.Forms rewrite, while not taking GNU/Linux into consideration, and using Catalyst for macOS MAUI backend, dotnet watch drama, some of the ASP.NET features seen as way to sell Azure stuff,....
If you look closer, you will notice that usually the React Native or Electron based applications are from business units that are mostly C++ focused, that never had great love for .NET in first place.
While the team tries to cater to new generations with making .NET development a great experience, even with some constraints in cross-platform deployments, I think they would gain more by fixing the bad perception .NET still gets in UNIX shops, which those upper management decisions don't make any better, regardless of how great .NET happens to be.
That said, the difference between the two has a lot less to do with the language itself than the world surrounding it. You can use Swift cross platform but it’s very obvious that Apple platforms are the primary target. Rust has a rich and varied package system, about the only assumption most packages make is that you’re using the Rust standard library. By comparison lot of Swift packages (which is a much smaller ecosystem anyway that’s slowly transitioning away from Cocapods, Carthage etc) will lean on OS APIs that won’t work if you compile for Linux or WASM[1].
I want Swift to be a more convenient Rust but it just isn’t there. e.g look at IBM abandoning Swift on the server not that long ago.
[1] for example, this blog post:
https://swiftrocks.com/weak-dictionary-values-in-swift
Discusses making a dictionary with weak values in Swift. It has a homegrown Swift version then discusses using NSMapTable… which isn’t available on Linux. But you wouldn’t know that reading the article because the assumption is that you’re running on an Apple platform.