Remove a number of unneeded nullability suppressions. (dotnet#85788)

* Fix nullability annotation of the JsonSerializer.Serialize methods.

* Remove a few more suppressions from the implementation.

* Revert annotations in the public APIs.

Port dotnet#77068 to 7.0

Update NuGet reference versions (dotnet#72451)

These references were still pulling in Newtonsoft.Json 9.0.1 causing
governance problems.

Also update a Microsoft.Build.Tasks.Core reference to use our defined
property for it.