No, nothing public to report yet. I can say that we are actively working now toward the goal of .NET 5/.NET 6 class library support in Unity. Since .NET 6 will be a long term support release from Microsoft, we will likely target .NET 6 instead of .NET 5 for the first .NET Core-based release of Unity, but that is still uncertain.
This is a bit outside of the area my team supports, so I’m not as sure about these questions. I know there have been some discussions about moving to .csproj files from .asmdef, but I don’t think there is any active work here yet. I doubt that Unity will have built-in support for nuget soon.
I don’t expect this to happen. From a class library perspective, I think Unity will support .NET FW (probably version 4.8), .NET Standard 2.1, and .NET 5/6 in the future. Although Unity has a pretty large C# API, I don’t expect us to try to publish a TFM now. In essence, that means the Unity API would only be available in Unity, and not via nuget, for example. That would still allow parity with the current approach Unity has. So although have a Unity TFM would be interesting, not having one doesn’t loose anything.
I’d love to have more details to share, but we’re not ready to announce roadmaps publicly at this time.