MudDialog with progress won't open while writing data to XML

I created a custom dialog component with MudProgressCircular (Child razor) that should display the progress while writing the part details to the XML output file. The issue I am trying to address is the dialog won't open while saving the details to the file, but it opens later when the task is complete.

Parent.razor

<MudButton Class="mt-2" OnClick="@(() => OnClickedAsync())"  Color="Color.Primary" Size="Size.Small" Edge="Edge.Start">Process Parts</MudButton>@code {    private List<Part> partItems;    private async Task OnClickedAsync()    {        using (var handler = new HttpClientHandler())        {            using (var httpClient = new HttpClient(handler))            {                serviceEndpoint = $"{Config.GetValue<string>("API")}/Parts";                var parts = await httpClient.GetFromJsonAsync<Part[]>(serviceEndpoint);                partItems = parts.ToList();            }        }        ProcessParts(partItems);    }    private void ProcessParts(List<Part> parts)    {        var options = new DialogOptions            {                FullWidth = true,                MaxWidth = MaxWidth.ExtraExtraLarge,                CloseButton = true,                Position = DialogPosition.Center,                CloseOnEscapeKey = true            };        var param = new DialogParameters();        param.Add("Parts", parts);        var dialogRef = Dialogsrv.Show<Child>($"Processing parts", param, options);}

Child.razor

<MudDialog Style="width:fit-content"><DialogContent><MudProgressCircular Color="Color.Primary" Value="@_value" Size="Size.Large">            @_value.ToString("N0") %</MudProgressCircular></DialogContent><DialogActions><MudButton Variant="Variant.Filled" Color="Color.Primary" OnClick="Close">Close</MudButton></DialogActions></MudDialog>@code {    [CascadingParameter]    private IMudDialogInstance ThisDialog { get; set; }    [Parameter] public List<Part> Parts { get; set; }    private int count = 0;    private double _value;    protected override void OnInitialized()    {        ProcessParts(Parts);    }    private void ProcessParts(List<Part> parts)    {        XDocument doc = XDocument.Load("Contents\\Template.xml");        XElement root = doc.Root;        foreach (var part in parts)        {            root.Element("Parts").Add(                new XElement("Part",                    new XElement("PartNo", part.Part),                    new XElement("Filename", part.FileName),                    new XElement("Material", part.Material),                    new XElement("CustomerName", part.CustomerName)            ));            count++;            _value = 100 * count / parts.Count;        }        string fullPath = Path.Combine(_filePath, "Parts.xml");        using (StreamWriter stream = new StreamWriter(fullPath, false, Encoding.GetEncoding("Windows-1252")))        {            doc.Save(stream);        }    }}

I made sure the following if anyone is wondering.

• MudDialogProvider exists in the MainLayout.razor
• Registered the dialog service in dependency injection

Then I thought this might be an async/await issue, so I switched the methods in the Child.razor to the synchronous, but no luck.