Chromium.AspNetCore.Bridge提供了一个解决方案，它使用owin在内存中托管服务器端代码，并提供一个RequestInterceptor来将所有请求干净地中继到“服务器”代码。
上面的链接有工作示例，但很简单：

App.xaml.cs：

private IWebHost _host;
private AppFunc _appFunc;

public AppFunc AppFunc
{
    get { return _appFunc; }
}

protected override void OnStartup(StartupEventArgs e)
{
    base.OnStartup(e);

    Environment.SetEnvironmentVariable("ASPNETCORE_ENVIRONMENT", "Development");

    _ = Task.Run(async () =>
      {
          var builder = new WebHostBuilder();

          builder.ConfigureServices(services =>
          {
              var server = new OwinServer();
              server.UseOwin(appFunc =>
              {
                  _appFunc = appFunc;
              });

              services.AddSingleton<IServer>(server);
          });

          _host = builder
              .UseStartup<Startup>()
              .UseContentRoot(Directory.GetCurrentDirectory())
              .Build();

          await _host.RunAsync();
      });            
}

MainWindow.xaml.cs

private AppFunc _appFunc;
public MainWindow()
{
    InitializeComponent();

    Browser.CoreWebView2InitializationCompleted += Browser_CoreWebView2InitializationCompleted;
}

private void Browser_CoreWebView2InitializationCompleted(object sender, CoreWebView2InitializationCompletedEventArgs e)
{
    if (e.IsSuccess)
    {
        _appFunc = ((App)Application.Current).AppFunc;
        Browser.CoreWebView2.WebResourceRequested += BrowserWebResourceRequestedAsync;
        Browser.CoreWebView2.AddWebResourceRequestedFilter("*", CoreWebView2WebResourceContext.All);
    }
}

private async void BrowserWebResourceRequestedAsync(object sender, CoreWebView2WebResourceRequestedEventArgs e)
{
    var deferral = e.GetDeferral();

    var request = new ResourceRequest(e.Request.Uri, e.Request.Method, e.Request.Headers, e.Request.Content);

    var response = await RequestInterceptor.ProcessRequest(_appFunc, request);

    var coreWebView2 = (CoreWebView2)sender;

    e.Response = coreWebView2.Environment.CreateWebResourceResponse(response.Stream, response.StatusCode, response.ReasonPhrase, response.GetHeaderString());

    deferral.Complete();
}