How to append to the existing csv inside a zip in C#

Question

I am trying to modify the existing CSV inside the zip but the following code ends up creating a zip file containing an empty CSV file.

string zipFilePath = "testZipFile.zip"
using (ZipArchive zip = ZipFile.Open(zipFilePath, ZipArchiveMode.Update))
{
    var file = new MemoryStream();
    ZipArchiveEntry entry = zip.GetEntry("NewEntry.csv");
    using (var outputStream = entry.Open())
    {
         outputStream.CopyTo(file);
    }

    entry.Delete();
    stream2.CopyTo(file);

    entry = zip.CreateEntry("NewEntry.csv", CompressionLevel.Fastest);
    using (var entryStream = entry.Open())
    {
        file.CopyTo(entryStream);
    }
}