Use NUnit built-ins for Settings Tests

In #6287 it was suggested to improve how JSON settings tests are structured. This issue tracks that suggestion

> Depending on the type of `Settings`, maybe this could be
```csharp
            Assert.That(output.Settings, Contains.Key(LocalManifestFiles));
```

_Originally posted by @florelis in https://github.com/microsoft/winget-cli/pull/6287#discussion_r3575314082_
            