C# is a "first class" language in Godot and doesn't need a GDExtension, but it's not compatible with web builds yet. There is a draft PR that includes C# support but it adds about +50 MB to a web export and is also missing a few features.
And even that doesn't add consoles support, is W4 that far?
I did not know that. Thanks for the info. I always use C# with Godot, but never had a use-case where i needed a web build.