CI/CD: Migrate away from nitz/publish-nuget and use dotnet commands

[Deadpikle]

We should be able to migrate away from nitz/publish-nuget usage and just use these commands:

dotnet restore ...
dotnet build ...
dotnet pack ...
dotnet nuget push ...

This would simplify the CI/CD use a little bit and allow us to make tweaks easier without relying on an external action that is not updated anymore.

I'd like to use variables or something to keep the code clean and just do things in a loop (or otherwise save the hassle of having those repeating lines of commands repeated a bunch of times). Not sure if that's possible off the top of my head in GitHub actions.

Note on WinForms: probably need a dotnet restore too, based on this run's output: https://github.com/NetSparkleUpdater/NetSparkle/actions/runs/12979626914/job/36195840714