Allowing Anonymous Authentication in IIS breaks Windows Authentication

In a aspnet.core application I added the following middleware:

app.Use(async (context, next) =>
{
    var authService = context.RequestServices.GetRequiredService<IAuthenticationService>();

    AuthenticateResult result = null;

    // Try JWT first
    if (context.Request.Headers.ContainsKey("Authorization"))
    {
        result = await authService.AuthenticateAsync(context, JwtBearerDefaults.AuthenticationScheme);
    }

    // If JWT fails or wasn't present, try Windows
    if (result == null || !result.Succeeded)
    {
        result = await authService.AuthenticateAsync(context, NegotiateDefaults.AuthenticationScheme);
    }

    if (result?.Succeeded == true)
    {
        context.User = result.Principal!;
    }

    await next();
});

I setup the Authentication Services like this:

services.AddAuthentication( options =>
{
    options.DefaultAuthenticateScheme = NegotiateDefaults.AuthenticationScheme;
})
.AddNegotiate()
.AddJwtBearer(JwtBearerDefaults.AuthenticationScheme, options =>
{
    options.TokenValidationParameters = new TokenValidationParameters
    {
        ValidateIssuer = true,
        ValidateAudience = true,
        ValidateLifetime = true,
        ValidateIssuerSigningKey = true,
        ValidIssuer = Configuration.GetValue<string>("TokenValidIssuer"),
        ValidAudience = Configuration.GetValue<string>("TokenValidAudience"),
        IssuerSigningKey = new SymmetricSecurityKey(Encoding.UTF8.GetBytes(Configuration.GetValue<string>("SuperSecretKey")))
    };
});

The app is hosted in IIS. The problem is that when I allow Anonymous Authentication in IIS together with the Windows one, the Windows Authentication in the middleware stops to work, the result is not authenticated. Can someone help me how to set the IIS?