For testing purposes, two web apps are set up, a "client" app (localhost) and a server app (Azure web app). The client sends an AJAX request to the server and receives a cookie in response. Then it makes another AJAX call to the server, but there's no cookie in the request, it's missing.

Here's the server configuration (CORS setup; https://localhost:44316 is my "client" URL):

public class Startup
{
    public Startup(IConfiguration configuration)
    {
        Configuration = configuration;
    }

    public IConfiguration Configuration { get; }

    public void ConfigureServices(IServiceCollection services)
    {
        services.AddCors(o => {
            o.AddPolicy("policy1", builder =>
                builder.WithOrigins("https://localhost:44316")
                    .AllowAnyMethod()
                    .AllowAnyHeader()
                    .AllowCredentials());
        });

        services.AddControllers();
    }

    public void Configure(IApplicationBuilder app, IWebHostEnvironment env)
    {
        app.UseHttpsRedirection();

        app.UseRouting();

        app.UseCors("policy1");

        app.UseAuthorization();

        app.UseEndpoints(endpoints =>
        {
            endpoints.MapControllers();
        });
    }
}

Here's the first controller, returning the cookie:

[Route("api/[controller]")]
[ApiController]
public class AController : ControllerBase
{
    [HttpPost]
    public IActionResult Post()
    {
        var cookieOptions = new CookieOptions
        {
            HttpOnly = true,
            Expires = DateTime.Now.AddMinutes(10),
            SameSite = SameSiteMode.None
        };
        Response.Cookies.Append("mykey", "myvalue", cookieOptions);

        return Ok();
    }
}

Here's the second controller, which should receive the cookie (but it doesn't):

[Route("api/[controller]")]
[ApiController]
public class BController : ControllerBase
{
    [HttpPost]
    public IActionResult Post()
    {
        var x = Request.Cookies;

        return Ok(JsonConvert.SerializeObject(x));
    }
}

And here's the calling script from the "client" (first and second call, respectively):

function Go()
{
    $.ajax({
        url: 'https://somewebsite.azurewebsites.net/api/a',
        type: 'post',
        xhrFields: {
            withCredentials: true
        },
        success: function (data, textStatus, jQxhr)
        {
            console.log(data);
        },
        error: function (jqXhr, textStatus, errorThrown)
        {
            console.log(errorThrown);
        }
    });
}

function Go2()
{
    $.ajax({
        url: 'https://somewebsite.azurewebsites.net/api/b',
        type: 'post',
        xhrFields: {
            withCredentials: true
        },
        success: function (data, textStatus, jQxhr)
        {
            console.log(data);
        },
        error: function (jqXhr, textStatus, errorThrown)
        {
            console.log(errorThrown);
        }
    });
}

Does anyone have an idea what could be the problem here?