This code is the skeleton I was looking for when I posed the question. It uses only facilities available in .NET Core.
var watcher = new BluetoothLEAdvertisementWatcher();
var logPath = System.IO.Path.GetTempFileName();
var logFile = System.IO.File.Create(logPath);
var logWriter = new System.IO.StreamWriter(logFile);
logWriter.WriteLine("Log message");
logWriter.Dispose();