Update GH Actions to use Trusted Publishing via NuGet

[ashneilson]

Since our NuGet Publishing Token has Expired and wish to avoid using API Token based publishing moving forward, we have a need to modify our NuGet Publishing from GitHub Actions process to avoid the burden of rotating tokens.

Let's adopt the Trusted Publishing approach that NuGet recommends: https://devblogs.microsoft.com/dotnet/enhanced-security-is-here-with-the-new-trust-publishing-on-nuget-org/