docs: add concurrency model documentation to ServerSession and _transition_state

Github-Issue: #1691

Author: dgenio

src/mcp/server/session.py

@@ -123,6 +123,17 @@ class ServerSession(
         types.ClientNotification,
     ]
 ):
+    """Server-side MCP session.
+
+    Concurrency model: incoming messages are processed sequentially by a single
+    ``_receive_loop`` task spawned in ``BaseSession.__aenter__``.  All state
+    transitions driven by messages (``_received_request``, ``_received_notification``)
+    therefore execute without concurrent interleaving.  The only other code path
+    that mutates ``_initialization_state`` is ``__aexit__``, which may overlap
+    briefly with the receive loop before the task group is cancelled; that path
+    already handles transition failures gracefully.
+    """
+
     _initialization_state: InitializationState = InitializationState.NotInitialized
     _client_params: types.InitializeRequestParams | None = None
     _experimental_features: ExperimentalServerSessionFeatures | None = None
@@ -172,6 +183,12 @@ def is_initialized(self) -> bool:
     def _transition_state(self, new_state: InitializationState) -> None:
         """Transition the session to a new state, validating the transition.
 
+        This method is intentionally synchronous (no ``await``), so under
+        cooperative scheduling no task switch can occur between the validity
+        check and the state assignment.  External synchronization is therefore
+        unnecessary as long as the single-consumer invariant documented on the
+        class holds.
+
         Args:
             new_state: The target state to transition to.