Fix C# examples in documentation

- Fix documentation after C# renames.
- Add missing `partial` in C# class declarations.
- Change `delta` parameter type to `double` in C#.
- Ensure parameters match base declaration.
- Use `$` string interpolation in C#.
- Fix invalid or outdated C# code.
- Changed some examples to follow our style guide more closely.

doc/classes/SceneTree.xml

@@ -74,10 +74,10 @@
 				    print("end")
 				[/gdscript]
 				[csharp]
-				public async void SomeFunction()
+				public async Task SomeFunction()
 				{
 				    GD.Print("start");
-				    await ToSignal(GetTree().CreateTimer(1.0f), "timeout");
+				    await ToSignal(GetTree().CreateTimer(1.0f), SceneTreeTimer.SignalName.Timeout);
 				    GD.Print("end");
 				}
 				[/csharp]