refactor(AuthClient): Enhance AuthClient with lazy initialization and connection error handling

- Replaced immediate connection start with lazy initialization via Lazy<Task<bool>>.
- Added IsConnected and ConnectionError properties to track connection status and errors.
- Introduced TryStartAsync method to safely attempt connection startup without throwing exceptions.

DigitalData.Auth.Abstractions/IAuthClient.cs

@@ -3,4 +3,6 @@
 public interface IAuthClient : IAuthClientHandler
 {
     Task StartAsync();
+
+    Task<bool> TryStartAsync();
 }

DigitalData.Auth.Client/AuthClient.cs

@@ -9,6 +9,8 @@ public class AuthClient : IAuthClient
 {
     private readonly HubConnection _connection;
 
+    private readonly Lazy<Task<bool>> _lazyInitiator;
+
     private readonly ILogger? _logger;
 
     private readonly ClientParams _params;
@@ -24,9 +26,42 @@ public class AuthClient : IAuthClient
         _logger = logger;
 
         _params = paramsOptions.Value;
+        
+        _lazyInitiator = new(async () =>
+        {
+            try
+            {
+                await _connection.StartAsync();
+                IsConnected = true;
+                return true;
+            }
+            catch(Exception ex)
+            {
+                ConnectionError = ex;
+                throw;
+            }
+        });
     }
 
-    public async Task StartAsync() => await _connection.StartAsync();
+    public bool IsConnected { get; private set; } = false;
+
+    public Exception? ConnectionError { get; private set; }
+
+    public bool IsConnectionFailed => ConnectionError is not null;
+
+    public async Task StartAsync() => await _lazyInitiator.Value;
+
+    public async Task<bool> TryStartAsync()
+    {
+        try
+        {
+            return await _lazyInitiator.Value;
+        }
+        catch
+        {
+            return false;
+        }
+    }
 
     public Task ReceiveMessageAsync(string user, string message) => Task.Run(() => _params.Events.OnMessageReceived(user, message, _logger));
 }