First install Saxon-HE, it looks like that it Saxon Home Edition does not support .NET core, which is why test project has to be .NET Framework.

Example method:

private static string ValidateXmlFile(string inputFile, string transformFile)
{
	try
	{
		if (string.IsNullOrWhiteSpace(inputFile))
		{
			throw new FileNotFoundException("Filename is empty");
		}

		inputFile = Path.GetFullPath(inputFile);
		if (!File.Exists(inputFile))
		{
			throw new FileNotFoundException($"File: {inputFile} not found");
		}

		transformFile = Path.GetFullPath(transformFile);
		if (!File.Exists(transformFile))
		{
			throw new FileNotFoundException($"File: {transformFile} not found");
		}

		Processor processor = new Processor();

		DocumentBuilder builder = processor.NewDocumentBuilder();
		builder.BaseUri = new Uri(inputFile);

		XdmNode inputNode;
		using (var inputStream = File.OpenRead(inputFile))
		{
			inputNode = builder.Build(inputStream);
		}

		XsltCompiler compiler = processor.NewXsltCompiler();
		XsltExecutable executable;
		using (var xsltStream = File.OpenRead(transformFile))
		{
			executable = compiler.Compile(xsltStream);
			if (compiler.GetErrorList().Count != 0)
				throw new Exception("Exception loading xsl!");
		}

		XsltTransformer transformer = executable.Load();

		transformer.InitialContextNode = inputNode;

		Serializer serializer = processor.NewSerializer();
		using (var stringWriter = new StringWriter())
		{
			serializer.SetOutputWriter(stringWriter);
			transformer.Run(serializer);
			string result = stringWriter.ToString();
			return result;
		}
	}
	catch (Exception e)
	{
	   return e.Message;
	}
}
Since validation result is XML, we can parse failed validations like:
IEnumerable<FailedAssert> failedAsserts = doc.Descendants(svrl + "failed-assert")
	.Select(fa => new FailedAssert
	{
		Flag = fa.Attribute("flag")?.Value,
		Id = fa.Attribute("id")?.Value,
		Test = fa.Attribute("test")?.Value,
		Location = fa.Attribute("location")?.Value,
		Text = fa.Element(svrl + "text")?.Value
	});
SVRL is an abbreviation for 'Schematron Validation Report Language.'

FailedAssert class looks like:

public class FailedAssert
{
	public string Flag { get; set; }
	public string Id { get; set; }
	public string Test { get; set; }
	public string Location { get; set; }
	public string ExceptionMessage { get; set; }
	public string Text { get; set; }
}
Example download from here. For this example I used file 01.03a-INVOICE_uncefact.xml which I downloaded from here where I manipulated with DateTimeField. Instead of a date I wrote "test", in order to trigger a failed assertion. I also downloaded XSL file EN16931-CII-validation.xsl from "Koordinierungsstelle für IT-Standards" (KoSIT) GitHub repository.