Executing PowerShell code at the API level

[Gintaras]

.NET 8.02 (which might include Newtonsoft.Json.dll version 13.01)

Normally .NET does not include Newtonsoft.Json.dll. Maybe the other Newtonsoft.Json.dll comes from another nuget package which is installed in another folder. If you can find that package, try to install it in the ps folder. The NuGet tool probably will pick the one that makes both nuget packages happy.