client: surface connection errors to callers

This commit allows blocking clients to receive a more informative error
message than "context deadline exceeded", which is especially helpful in
tracking down persistent client misconfiguration (such as an invalid TLS
certificate, an invalid server that's refusing connections, etc.)

clientconn.go

@@ -216,7 +216,14 @@ func DialContext(ctx context.Context, target string, opts ...DialOption) (conn *
 	defer func() {
 		select {
 		case <-ctx.Done():
-			conn, err = nil, ctx.Err()
+			switch {
+			case ctx.Err() == err:
+				conn = nil
+			case err == nil:
+				conn, err = nil, ctx.Err()
+			default:
+				conn, err = nil, fmt.Errorf("%v: %v", ctx.Err(), err)
+			}
 		default:
 		}
 	}()
@@ -321,6 +328,9 @@ func DialContext(ctx context.Context, target string, opts ...DialOption) (conn *
 			}
 			if !cc.WaitForStateChange(ctx, s) {
 				// ctx got timeout or canceled.
+				if err = cc.blockingpicker.connectionError(); err != nil {
+					return nil, err
+				}
 				return nil, ctx.Err()
 			}
 		}

clientconn_test.go

@@ -229,8 +229,9 @@ func (s) TestDialWaitsForServerSettingsAndFails(t *testing.T) {
 		client.Close()
 		t.Fatalf("Unexpected success (err=nil) while dialing")
 	}
-	if err != context.DeadlineExceeded {
-		t.Fatalf("DialContext(_) = %v; want context.DeadlineExceeded", err)
+	expectedMsg := "server handshake"
+	if !strings.Contains(err.Error(), context.DeadlineExceeded.Error()) || !strings.Contains(err.Error(), expectedMsg) {
+		t.Fatalf("DialContext(_) = %v; want a message that includes both %q and %q", err, context.DeadlineExceeded.Error(), expectedMsg)
 	}
 	<-done
 	if numConns < 2 {