Be happy to find out I’m wrong.
The way unity solves this is with some kind of proprietary compiler. They translate the C# into C++, and then compile that into webassembly.
Whereas others (incl. Godot) need to ship the .NET runtime in the browser. (A VM in a VM.)
It makes me sad that Unity doesn't open source that. That would be amazing.
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Be happy to find out I’m wrong.