Fix WebSocket handshake error handling and unnecessary token refresh

supervisor/homeassistant/api.py

@@ -219,7 +219,7 @@ async def connect_websocket(
                     self._access_token,
                     max_msg_size=max_msg_size,
                 )
-            except HomeAssistantAPIError:
+            except HomeAssistantAuthError:
                 self._access_token = None
                 if attempt == 2:
                     raise

supervisor/homeassistant/websocket.py

@@ -185,7 +185,7 @@ async def connect(
             TimeoutError,
         ) as err:
             await client.close()
-            raise HomeAssistantAPIError(
+            raise HomeAssistantWSConnectionError(
                 f"Unexpected error during WebSocket handshake: {err}"
             ) from err
 
@@ -234,7 +234,7 @@ async def connect_with_auth(
             TimeoutError,
         ) as err:
             await client.close()
-            raise HomeAssistantAPIError(
+            raise HomeAssistantWSConnectionError(
                 f"Unexpected error during WebSocket handshake: {err}"
             ) from err
 
@@ -309,7 +309,7 @@ async def _async_send_command(self, message: dict[str, Any]) -> None:
         try:
             await self._ensure_connected()
         except HomeAssistantWSError as err:
-            _LOGGER.debug("Can't send WebSocket command: %s", err)
+            _LOGGER.warning("Can't send WebSocket command: %s", err)
             return
 
         # _ensure_connected guarantees self.client is set