fix silent onboarding drop-off in /addgamer flow

Set awaiting_addgamer_username as soon as the menu is shown so typing a
username directly (without tapping the button) is handled instead of
being silently ignored. Also stop reporting a valid username as "not
found" when Lichess returns a non-404 error (rate limit/timeout), and
surface an error message if the addgamer menu itself fails to send.

LichessClientTG_bot/lichess_api.py

@@ -145,8 +145,15 @@ class LichessAPI:
             logger.error(f"Error getting puzzles period: {e}")
             return None
     
-    async def check_user_exists(self, username: str) -> bool:
-        """Check if user exists on Lichess"""
+    async def check_user_exists(self, username: str) -> Optional[bool]:
+        """
+        Check if user exists on Lichess.
+
+        Returns True/False for a definitive answer (200/404), or None if the
+        check itself failed (rate limit, network error, unexpected status) —
+        callers must not treat None as "not found", since the username may
+        well be valid.
+        """
         await self.rate_limiter.wait_if_needed()
         try:
             async with aiohttp.ClientSession() as session:
@@ -160,10 +167,10 @@ class LichessAPI:
                         return False
                     else:
                         logger.error(f"Failed to check user existence: {response.status}")
-                        return False
+                        return None
         except Exception as e:
             logger.error(f"Error checking user existence: {e}")
-            return False
+            return None
     
     async def get_user_ratings(self, username: str) -> Optional[Dict[str, Any]]:
         """Get user ratings from Lichess API"""