Support ClientSDK in Unity

[Fregnen]

Coming from support ticket #78813.

Is your feature request related to a problem? Please describe.
We would like to see the Launch Darkly Client SDK support Unity.
My attempt to implement LaunchDarkly .NET ClientSDK 5.2.1, imported with NuGet for Unity, did unfortunately not work. Issue is, that the SDK has a dependency on System.Text.Json (>=6.0.0), which when serializing from LDjson to json, giving following error:
System.TypeLoadException: VTable setup of type System.Text.Json.Utf8JsonWriter failed

I have taken inspiration from this repo but without luck (I have updated it to Context instead of User).

Describe alternatives you've considered
See support ticket #78813.