[workspace] Upgrade meshcat to latest commit (RobotLocomotion#21313)

Author: jwnimmer-tri

geometry/test/meshcat_manual_test.cc

@@ -450,6 +450,11 @@ Ignore those for now; we'll need to circle back and fix them later.
     const double table_height = 0.7645;
     plant.WeldFrames(plant.world_frame(), plant.GetFrameByName("link"),
                      RigidTransformd(Vector3d{0, 0, -table_height - 0.01}));
+    parser.AddModelsFromUrl(
+        "package://drake_models/ycb/006_mustard_bottle.sdf");
+    plant.WeldFrames(plant.world_frame(),
+                     plant.GetFrameByName("base_link_mustard"),
+                     RigidTransformd(Vector3d{0, -0.3, 0.01}));
     plant.Finalize();
 
     builder.ExportInput(plant.get_actuation_input_port(), "actuation_input");
@@ -469,7 +474,8 @@ Ignore those for now; we'll need to circle back and fix them later.
 
     diagram->ForcedPublish(*context);
     std::cout
-        << "- Now you should see a kuka model (from MultibodyPlant/SceneGraph)"
+        << "- Now you should see a kuka model (from MultibodyPlant/SceneGraph) "
+           "and a mustard bottle lying on its side, with the label facing up."
         << std::endl;
 
     MaybePauseForUser();
@@ -508,6 +514,7 @@ Ignore those for now; we'll need to circle back and fix them later.
          "- the camera is focused on the contact point between the robot and "
          "table,\n"
          "- the iiwa is visible,\n"
+         "- the mustard bottle visible including its texture (front label),\n"
          "- the animation plays,\n"
          "- the environment map is present, and\n"
          "- the browser Console has no warnings nor errors\n"

tools/workspace/meshcat/repository.bzl

@@ -10,8 +10,8 @@ def meshcat_repository(
         Updating this commit requires local testing; see
         drake/tools/workspace/meshcat/README.md for details.
         """,
-        commit = "e87530b45282872a07dd164351aa4dfef40d9f5b",
-        sha256 = "d15ba8fa1dca154266bd44265e38bce9fd34db4e5ac9a1dcced639d1c78eef9f",  # noqa
+        commit = "601b55df0839430297ae53503ea2c61e4cdf1314",
+        sha256 = "c1b006483773ad435acba17def30d3359eb39bf7c859fcfbcfd8baca006def37",  # noqa
         build_file = ":package.BUILD.bazel",
         mirrors = mirrors,
     )