feat: add SRP authentication, improve security

- Replace RSA key exchange with SRP (Secure Remote Password)
- Password never transmitted over network
- Add unit tests for endpoints
- Fix datetime.UTC compatibility for Python < 3.11
- Fix logger.exception usage
- Update README with new auth flow diagram

cmd_chat/server/managers.py

@@ -28,8 +28,8 @@ class ConnectionManager:
                     continue
                 try:
                     await connection.send(message)
-                except Exception as e:
-                    logger.warning(f"Failed to send message to {user_id}: {e}")
+                except Exception:
+                    logger.exception(f"Failed to send message to {user_id}")
                     disconnected.append(user_id)
 
             for user_id in disconnected:
@@ -42,7 +42,7 @@ class ConnectionManager:
                 try:
                     await connection.send(message)
                     return True
-                except Exception as e:
-                    logger.warning(f"Failed to send personal message to {user_id}: {e}")
+                except Exception:
+                    logger.exception(f"Failed to send personal message to {user_id}")
                     return False
         return False