Keep _on_request private, expose it via an on_request property

Mirror the on_notify/_on_notify split rather than making the worker
method public.

Author: Kludex

src/mcp/server/context.py

@@ -125,7 +125,7 @@ async def log(self, level: LoggingLevel, data: Any, logger: str | None = None, *
 class ServerMiddleware(Protocol[_MwLifespanT]):
     """Context-tier middleware: `(ctx, call_next) -> result`.
 
-    Runs at the top of `ServerRunner.on_request` / `_on_notify` after `ctx`
+    Runs at the top of `ServerRunner._on_request` / `_on_notify` after `ctx`
     is built but before any validation, lookup, or handshake. Wraps every
     inbound request and notification: `initialize`, the pre-init gate,
     `METHOD_NOT_FOUND`, params validation, the handler call, and

src/mcp/server/lowlevel/server.py

@@ -231,7 +231,7 @@ def __init__(
         self._session_manager: StreamableHTTPSessionManager | None = None
         # Context-tier middleware: wraps every inbound request (including
         # `initialize`, lookup, validation, handler) with
-        # `(ctx, call_next)`. Applied in `ServerRunner.on_request`.
+        # `(ctx, call_next)`. Applied in `ServerRunner._on_request`.
         # `OpenTelemetryMiddleware` ships on by default so every server emits a
         # SERVER span per message; it is a no-op until an OTel exporter is
         # installed. Drop it from this list to opt out.

src/mcp/server/runner.py

@@ -142,11 +142,15 @@ class ServerRunner(Generic[LifespanT]):
     init_options: InitializationOptions | None = None
     """`InitializeResult` payload. Defaults to `server.create_initialization_options()`."""
 
+    @cached_property
+    def on_request(self) -> OnRequest:
+        return self._on_request
+
     @cached_property
     def on_notify(self) -> OnNotify:
         return self._on_notify
 
-    async def on_request(
+    async def _on_request(
         self,
         dctx: DispatchContext[TransportContext],
         method: str,
@@ -263,7 +267,7 @@ async def _inner(ctx: ServerRequestContext[LifespanT, Any]) -> None:
     def _compose_server_middleware(self, inner: CallNext) -> CallNext:
         """Wrap `inner` in `Server.middleware`, outermost-first.
 
-        Shared by `on_request` and `_on_notify` so the same middleware chain
+        Shared by `_on_request` and `_on_notify` so the same middleware chain
         observes every inbound message. The composed callable takes the `ctx`
         at call time, so a middleware can rewrite it for the rest of the chain.
         """
@@ -338,7 +342,7 @@ def _negotiate_initialize(params: Mapping[str, Any] | None) -> tuple[InitializeR
         return init, negotiated
 
     def _handle_initialize(self, params: Mapping[str, Any] | None) -> InitializeResult:
-        """Build the `initialize` result; state commits later in `on_request`."""
+        """Build the `initialize` result; state commits later in `_on_request`."""
         _, negotiated = self._negotiate_initialize(params)
         opts = self.init_options if self.init_options is not None else self.server.create_initialization_options()
         return InitializeResult(