Open meshcat-server before code execution to improve easiness in visualization (v1.5.0)?

I’m learning pydrake via their tutorials executing it locally in my pc (pydrake pip version). I’ve changed the code from simple pendulum to use Meshcat locally instead of in the notebook with:

from pydrake.systems.framework import DiagramBuilder
from pydrake.examples.pendulum import PendulumPlant, PendulumGeometry
from pydrake.geometry import MeshcatVisualizer
from pydrake.systems.analysis import Simulator
from pydrake.geometry import Meshcat
import webbrowser

builder = builder.AddSystem(PendulumPlant())
scene_graph = builder.AddSystem(SceneGraph())
PendulumGeometry.AddToBuilder(builder, pendulum.get_state_output_port(), scene_graph)
meshcat = Meshcat(port=7001)
MeshcatVisualizer.AddToBuilder(builder, scene_graph, meshcat)
meshcat.Set2dRenderMode(X_WC=RigidTransform(RotationMatrix.MakeZRotation(np.pi), [0, 1, 0]))
diagram = builder.Build()
simulator = Simulator(diagram)
context = simulator.get_mutable_context()
context.SetContinuousState([0.5, 0])
simulator.set_target_realtime_rate(1.0)
while True:
    simulator.AdvanceTo(simulator.get_context().get_time() + 1.0)

But there is an inconvenience with the server (or the web page) popping up. I need to refresh each time I execute the code to be able to see the simulation. Is there a way to see the simulation automatically without the need to refresh the webpage? (version 1.5.0 of drake via pip)

I’m looking to connect like in a previous version with meshcat-server terminal command and later connecting it in code.
Right now I’m using the webbrowser module to open a new tab each time I execute the code, but I end up with a lot of tabs at the end of some testing.