In the WebAssembly App project add this code to add the cookie using the HttpClient in program.cs file:

using BlazorWebAssemblyApp1;
using Microsoft.AspNetCore.Components.Web;
using Microsoft.AspNetCore.Components.WebAssembly.Hosting;

var builder = WebAssemblyHostBuilder.CreateDefault(args);
builder.RootComponents.Add<App>("#app");
builder.RootComponents.Add<HeadOutlet>("head::after");

var httpClientHandler = new HttpClientHandler();
httpClientHandler.CookieContainer = new System.Net.CookieContainer();

var httpClient = new HttpClient(httpClientHandler)
{
    BaseAddress = new Uri(builder.HostEnvironment.BaseAddress)
};

builder.Services.AddScoped(sp => new HttpClient { BaseAddress = new Uri(builder.HostEnvironment.BaseAddress) });

await builder.Build().RunAsync();

Code to fetch cookie:

@page "/fetch-cookies"
    @inject CookieService CookieService

<h3>Fetch Cookies</h3>

<button @onclick="FetchCookies">Fetch Cookies</button>

@if (!string.IsNullOrEmpty(LaxCookie))
{
    <p>Lax Cookie: @LaxCookie</p>
}

@if (!string.IsNullOrEmpty(StrictCookie))
{
    <p>Strict Cookie: @StrictCookie</p>
}

@code {
    private string LaxCookie;
    private string StrictCookie;

    private async Task FetchCookies()
    {
        LaxCookie = await CookieService.GetCookieAsync("SameSiteCookieLax");
        StrictCookie = await CookieService.GetCookieAsync("SameSiteCookieStrict");
    }
    }

Cookie.js :

window.blazorExtensions = {
       GetCookie: function (name) {
           let value = "; " + document.cookie;
           let parts = value.split("; " + name + "=");
           if (parts.length === 2) return parts.pop().split(";").shift();
       }
   };

CookieService.cs:(To get the cookie from browser)

using Microsoft.JSInterop;
    using System.Threading.Tasks;

    public class CookieService
    {
        private readonly IJSRuntime _jsRuntime;

        public CookieService(IJSRuntime jsRuntime)
        {
            _jsRuntime = jsRuntime;
        }

        public async Task<string> GetCookieAsync(string name)
        {
            return await _jsRuntime.InvokeAsync<string>("blazorExtensions.GetCookie", name);
        }
    }
    ```

    Add a JavaScript file (`wwwroot/cookies.js`) with the following content:

    ```javascript
    window.blazorExtensions = {
        GetCookie: function (name) {
            let value = "; " + document.cookie;
            let parts = value.split("; " + name + "=");
            if (parts.length === 2) return parts.pop().split(";").shift();
        }
    };

Do not forgot to add js file in index file:

In the sever size program.cs file set cors policy to configure CORS to allow the Blazor WebAssembly app to access it and set a cookie with a specific SameSite policy

using BlazorServerApp.Data;
using Microsoft.AspNetCore.Components;
using Microsoft.AspNetCore.Components.Web;

var builder = WebApplication.CreateBuilder(args);

// Add services to the container.
builder.Services.AddRazorPages();
builder.Services.AddServerSideBlazor();
builder.Services.AddSingleton<WeatherForecastService>();

builder.Services.AddCors(options =>
{
    options.AddPolicy("AllowBlazorClient",
        builder => builder
            .WithOrigins("https://localhost:7112") // URL of your Blazor WebAssembly app
            .AllowAnyMethod()
            .AllowAnyHeader()
            .AllowCredentials());
});


var app = builder.Build();

// Configure the HTTP request pipeline.
if (!app.Environment.IsDevelopment())
{
    app.UseExceptionHandler("/Error");
    // The default HSTS value is 30 days. You may want to change this for production scenarios, see https://aka.ms/aspnetcore-hsts.
    app.UseHsts();
}

app.UseHttpsRedirection();

app.UseStaticFiles();

app.UseRouting();

app.UseCors("AllowBlazorClient");

app.Use(async (context, next) =>
{
    context.Response.Cookies.Append("SameSiteCookieLax", "lax_value", new CookieOptions { SameSite = SameSiteMode.Lax });
    context.Response.Cookies.Append("SameSiteCookieStrict", "strict_value", new CookieOptions { SameSite = SameSiteMode.Strict });
    await next.Invoke();
});


app.MapBlazorHub();
app.MapFallbackToPage("/_Host");

app.Run();