mcp: set default logging level to info (#411)

During initialization, the default logging level is set to info allowing
servers to emit logs immediately without waiting for a client to set a
log level.
The updated example shows how to send a notification in the context of
the request.

Fixes #387

mcp/streamable.go

@@ -282,6 +282,7 @@ func (h *StreamableHTTPHandler) ServeHTTP(w http.ResponseWriter, req *http.Reque
 			if !hasInitialized {
 				state.InitializedParams = new(InitializedParams)
 			}
+			state.LogLevel = "info"
 			connectOpts = &ServerSessionOptions{
 				State: state,
 			}