PYTHON-5421 Fix handling of client timeout property (mongodb#2240)

Author: blink1073

pymongo/asynchronous/mongo_client.py

@@ -758,6 +758,7 @@ def __init__(
         self._host = host
         self._port = port
         self._topology: Topology = None  # type: ignore[assignment]
+        self._timeout: float | None = None
 
         # _pool_class, _monitor_class, and _condition_class are for deep
         # customization of PyMongo, e.g. Motor.

pymongo/synchronous/mongo_client.py

@@ -756,6 +756,7 @@ def __init__(
         self._host = host
         self._port = port
         self._topology: Topology = None  # type: ignore[assignment]
+        self._timeout: float | None = None
 
         # _pool_class, _monitor_class, and _condition_class are for deep
         # customization of PyMongo, e.g. Motor.