It’s surprising to me that javascript wasn’t chosen as the scripting language for all these gaming engines. Though I do see the benefit of C# being typed and compiled.
Microsoft XNA used to be a popular indie game framework that used C#. Stardew Valley, Celeste and Terraria run on XNA.
Mono used C#. Xamarin used Mono to create a cross-platform application framework that worked on mobile. Unity leveraged Xamarin to create a cross-platform game engine that worked on mobile, ending up using C#.
Thus, two generations of indie gamedevs ended up learning C# to create games. Then Unity grew a whole lot, so more and more people ended up associating C# with game engines, so as soon as Godot was released people started asking for C# support.
But C# being the language of choice doesn't really depend on specific C# features. It could've just as easily been Lua or JavaScript instead. For example, RPG Maker moved from Ruby to JavaScript when they upgraded to a new engine, again, because their new rendering engine was nw.js, and getting it to run almost anywhere was easy.