mcp: fix stray log.Printf in notifySessions

I encountered these logs, and they were distracting and noisy. We
shouldn't log to stderr unless configured by the user. Thread through
the logger.

Also, use ensureLogger in the streamable client to simplify call sites.

Updates #708
Updates #684

mcp/client.go

@@ -10,6 +10,7 @@ import (
 	"errors"
 	"fmt"
 	"iter"
+	"log/slog"
 	"slices"
 	"strings"
 	"sync"
@@ -26,6 +27,7 @@ import (
 type Client struct {
 	impl                    *Implementation
 	opts                    ClientOptions
+	logger                  *slog.Logger // TODO: file proposal to export this
 	mu                      sync.Mutex
 	roots                   *featureSet[*Root]
 	sessions                []*ClientSession
@@ -46,6 +48,7 @@ func NewClient(impl *Implementation, opts *ClientOptions) *Client {
 	}
 	c := &Client{
 		impl:                    impl,
+		logger:                  ensureLogger(nil), // ensure we have a logger
 		roots:                   newFeatureSet(func(r *Root) string { return r.URI }),
 		sendingMethodHandler_:   defaultSendingMethodHandler,
 		receivingMethodHandler_: defaultReceivingMethodHandler[*ClientSession],
@@ -341,7 +344,7 @@ func changeAndNotify[P Params](c *Client, notification string, params P, change
 		sessions = slices.Clone(c.sessions)
 	}
 	c.mu.Unlock()
-	notifySessions(sessions, notification, params)
+	notifySessions(sessions, notification, params, c.logger)
 }
 
 func (c *Client) listRoots(_ context.Context, req *ListRootsRequest) (*ListRootsResult, error) {