Replace custom socket implementation with SignalR.

Replace MSAL and custom cookie auth with Microsoft.Identity.EntityFramework
Also some UI redesign to accommodate different login experience.

Shogi.UI/Shared/ShogiApi.cs

@@ -0,0 +1,74 @@
+using Shogi.Contracts.Api;
+using Shogi.Contracts.Types;
+using System.Net;
+using System.Net.Http.Json;
+using System.Reflection.Metadata.Ecma335;
+using System.Text.Json;
+
+namespace Shogi.UI.Shared;
+
+public class ShogiApi(HttpClient httpClient)
+{
+	private readonly JsonSerializerOptions serializerOptions = new JsonSerializerOptions(JsonSerializerDefaults.Web);
+
+	public async Task Register(string email, string password)
+	{
+		var response = await httpClient.PostAsJsonAsync(Relative("register"), new { email, password });
+		response.EnsureSuccessStatusCode();
+	}
+
+	public async Task LoginEventArgs(string email, string password)
+	{
+		var response = await httpClient.PostAsJsonAsync("login?useCookies=true", new { email, password });
+		response.EnsureSuccessStatusCode();
+	}
+
+	public async Task Logout()
+	{
+		var response = await httpClient.PutAsync(Relative("User/GuestLogout"), null);
+		response.EnsureSuccessStatusCode();
+	}
+
+	public async Task<Session?> GetSession(string name)
+	{
+		var response = await httpClient.GetAsync(Relative($"Sessions/{name}"));
+		if (response.IsSuccessStatusCode)
+		{
+			return (await response.Content.ReadFromJsonAsync<Session>(this.serializerOptions));
+		}
+		return null;
+	}
+
+	public async Task<SessionMetadata[]> GetAllSessionsMetadata()
+	{
+		var response = await httpClient.GetAsync(Relative("Sessions"));
+		if (response.IsSuccessStatusCode)
+		{
+			return (await response.Content.ReadFromJsonAsync<SessionMetadata[]>(this.serializerOptions))!;
+		}
+		return [];
+	}
+
+	/// <summary>
+	/// Returns false if the move was not accepted by the server.
+	/// </summary>
+	public async Task<bool> Move(string sessionName, MovePieceCommand command)
+	{
+		var response = await httpClient.PatchAsync(Relative($"Sessions/{sessionName}/Move"), JsonContent.Create(command));
+		return response.IsSuccessStatusCode;
+	}
+
+	public async Task<string?> PostSession()
+	{
+		var response = await httpClient.PostAsync(Relative("Sessions"), null);
+		var sessionId = response.IsSuccessStatusCode ? await response.Content.ReadAsStringAsync() : null;
+		return sessionId;
+	}
+
+	public Task<HttpResponseMessage> PatchJoinGame(string name)
+	{
+		return httpClient.PatchAsync(Relative($"Sessions/{name}/Join"), null);
+	}
+
+	private static Uri Relative(string path) => new(path, UriKind.Relative);
+}